## Proving that Quantum Entanglement is Real

A Q&A with Caltech alumnus John Clauser on his first experimental proof of quantum entanglement

In the 1930s when scientists, including Albert Einstein and Erwin Schrödinger, first discovered the phenomenon of entanglement, they were perplexed. Entanglement, disturbingly, required two separated particles to remain connected without being in direct contact. Einstein famously called entanglement "spooky action at a distance," since the particles seemed to be communicating faster than the speed of light.

To explain the bizarre implications of entanglement, Einstein, along with Boris Podolsky and Nathan Rosen (EPR), argued that "hidden variables" should be added to quantum mechanics to explain entanglement, and to restore "locality" and "causality" to the behavior of the particles. Locality states that objects are only influenced by their immediate surroundings. Causality states that an effect cannot occur before its cause, and that causal signaling cannot propagate faster than light-speed. Niels Bohr famously disputed EPR's argument, while Schrödinger and Wendell Furry, in response to EPR, independently hypothesized that entanglement vanishes with wide-particle separation.

Unfortunately, no experimental evidence for or against quantum entanglement of widely separated particles was available then. Experiments have since proven that entanglement is very real and fundamental to nature. Moreover, quantum mechanics has now been proven to work, not only at very short distances but also at very great distances. Indeed, China's quantum-encrypted communications satellite, Micius, relies on quantum entanglement between photons that are separated by thousands of kilometers.

The very first of these experiments was proposed and executed by Caltech alumnus John Clauser (BS '64) in 1969 and 1972, respectively. His findings are based on Bell's theorem, devised by CERN theorist John Bell. In 1964, Bell ironically proved that EPR's argument actually led to the opposite conclusion from what EPR had originally intended to show. Bell showed that quantum entanglement is, in fact, incompatible with EPR's notion of locality and causality.

In 1969 , while still a graduate student at Columbia University, Clauser, along with Michael Horne, Abner Shimony, and Richard Holt, transformed Bell's 1964 mathematical theorem into a very specific experimental prediction via what is now called the Clauser–Horne–Shimony–Holt (CHSH) inequality ( Their paper has been cited more than 8,500 times on Google Scholar .) In 1972, when he was a postdoctoral researcher at UC Berkeley and Lawrence Berkeley National Laboratory, Clauser and graduate student Stuart Freedman were the first to prove experimentally that two widely separated particles (about 10 feet apart) can be entangled. Clauser went on to perform three more experiments testing the foundations of quantum mechanics and entanglement, with each new experiment confirming and extending his results. The Freedman–Clauser experiment was the first test of the CHSH inequality. It has now been tested experimentally hundreds of times at laboratories around the world to confirm that quantum entanglement is real.

Clauser's work earned him the 2010 Wolf Prize in physics. He shared it with Alain Aspect of the Institut d' Optique and Ecole Polytechnique and Anton Zeilinger of the University of Vienna and the Austrian Academy of Sciences "for an increasingly sophisticated series of tests of Bell's inequalities, or extensions thereof, using entangled quantum states," according to the award citation.

Here, John Clauser answers questions about his historical experiments.

## We hear that your idea of testing the principles of entanglement was unappealing to other physicists. Can you tell us more about that?

In the 1960s and 70s, experimental testing of quantum mechanics was unpopular at Caltech, Columbia, UC Berkeley, and elsewhere. My faculty at Columbia told me that testing quantum physics was going to destroy my career. While I was performing the 1972 Freedman–Clauser experiment at UC Berkeley, Caltech's Richard Feynman was highly offended by my impertinent effort and told me that it was tantamount to professing a disbelief in quantum physics. He arrogantly insisted that quantum mechanics is obviously correct and needs no further testing! My reception at UC Berkeley was lukewarm at best and was only possible through the kindness and tolerance of Professors Charlie Townes [PhD '39, Nobel Laureate '64] and Howard Shugart [BS '53], who allowed me to continue my experiments there.

In my correspondence with John Bell , he expressed exactly the opposite sentiment and strongly encouraged me to do an experiment. John Bell's 1964 seminal work on Bell's theorem was originally published in the terminal issue of an obscure journal, Physics , and in an underground physics newspaper, Epistemological Letters . It was not until after the 1969 CHSH paper and the 1972 Freedman–Clauser results were published in the Physical Review Letters that John Bell finally openly discussed his work. He was aware of the taboo on questioning quantum mechanics' foundations and had never discussed it with his CERN co-workers.

## What made you want to carry through with the experiments anyway?

Part of the reason that I wanted to test the ideas was because I was still trying to understand them. I found the predictions for entanglement to be sufficiently bizarre that I could not accept them without seeing experimental proof. I also recognized the fundamental importance of the experiments and simply ignored the career advice of my faculty. Moreover, I was having a lot of fun doing some very challenging experimental physics with apparatuses that I built mostly using leftover physics department scrap. Before Stu Freedman and I did the first experiment, I also personally thought that Einstein's hidden-variable physics might actually be right, and if it is, then I wanted to discover it. I found Einstein's ideas to be very clear. I found Bohr's rather muddy and difficult to understand.

## What did you expect to find when you did the experiments?

In truth, I really didn't know what to expect except that I would finally determine who was right—Bohr or Einstein. I admittedly was betting in favor of Einstein but did not actually know who was going to win. It's like going to the racetrack. You might hope that a certain horse will win, but you don't really know until the results are in. In this case, it turned out that Einstein was wrong. In the tradition of Caltech's Richard Feynman and Kip Thorne [BS '62], who would place scientific bets, I had a bet with quantum physicist Yakir Aharonov on the outcome of the Freedman–Clauser experiment. Curiously, he put up only one dollar to my two. I lost the bet and enclosed a two-dollar bill and congratulations when I mailed him a preprint with our results.

I was very sad to see that my own experiment had proven Einstein wrong. But the experiment gave a 6.3-sigma result against him [a five-sigma result or higher is considered the gold standard for significance in physics]. But then Dick Holt and Frank Pipkin's competing experiment at Harvard (never published) got the opposite result. I wondered if perhaps I had overlooked some important detail. I went on alone at UC Berkeley to perform three more experimental tests of quantum mechanics. All yielded the same conclusions. Bohr was right, and Einstein was wrong. The Harvard result did not repeat and was faulty. When I reconnected with my Columbia faculty, they all said, "We told you so! Now stop wasting money and go do some real physics." At that point in my career, the only value in my work was that it demonstrated that I was a reasonably talented experimental physicist. That fact alone got me a job at Lawrence Livermore National Lab doing controlled-fusion plasma physics research.

## Can you help us understand exactly what your experiments showed?

In order to clarify what the experiments showed, Mike Horne and I formulated what is now known as Clauser–Horne Local Realism [ 1974 ]. Additional contributions to it were subsequently offered by John Bell and Abner Shimony , so perhaps it is more properly called Bell–Clauser–Horne–Shimony Local Realism . Local Realism was very short-lived as a viable theory. Indeed, it was experimentally refuted even before it was fully formulated. Nonetheless, Local Realism is heuristically important because it shows in detail what quantum mechanics is not .

Local Realism assumes that nature consists of stuff, of objectively real objects, i. e., stuff you can put inside a box. (A box here is an imaginary closed surface defining separated inside and outside volumes.) It further assumes that objects exist whether or not we observe them. Similarly, definite experimental results are assumed to obtain, whether or not we look at them. We may not know what the stuff is, but we assume that it exists and that it is distributed throughout space. Stuff may evolve either deterministically or stochastically. Local Realism assumes that the stuff within a box has intrinsic properties, and that when someone performs an experiment within the box, the probability of any result that obtains is somehow influenced by the properties of the stuff within that box. If one performs say a different experiment with different experimental parameters, then presumably a different result obtains. Now suppose one has two widely separated boxes, each containing stuff. Local Realism further assumes that the experimental parameter choice made in one box cannot affect the experimental outcome in the distant box. Local Realism thereby prohibits spooky action-at-a-distance. It enforces Einstein's causality that prohibits any such nonlocal cause and effect. Surprisingly, those simple and very reasonable assumptions are sufficient on their own to allow derivation of a second important experimental prediction limiting the correlation between experimental results obtained in the separated boxes. That prediction is the 1974 Clauser–Horne (CH) inequality.

The 1969 CHSH inequality's derivation had required several minor supplementary assumptions, sometimes called "loopholes." The CH inequality's derivation eliminates those supplementary assumptions and is thus more general. Quantum entangled systems exist that disagree with the CH prediction, whereby Local Realism is amenable to experimental disproof. The CHSH and CH inequalities are both violated, not only by the first 1972 Freedman–Clauser experiment and my second 1976 experiment but now by literally hundreds of confirming independent experiments. Various labs have now entangled and violated the CHSH inequality with photon pairs, beryllium ion pairs, ytterbium ion pairs, rubidium atom pairs, whole rubidium-atom cloud pairs, nitrogen vacancies in diamonds, and Josephson phase qubits.

Testing Local Realism and the CH inequality was considered by many researchers to be important to eliminate the CHSH loopholes. Considerable effort was thus marshaled, as quantum optics technology improved and permitted. Testing the CH inequality had become a holy grail challenge for experimentalists. Violation of the CH inequality was finally achieved first in 2013 and again in 2015 at two competing laboratories: Anton Zeilinger's group at the University of Vienna, and Paul Kwiat's group at the University of Illinois at Urbana–Champaign. The 2015 experiments involved 56 researchers! Local Realism is now soundly refuted! The agreement between the experiments and quantum mechanics now firmly proves that nonlocal quantum entanglement is real.

## What are some of the important technological applications of your work?

One application of my work is to the simplest possible object defined by Local Realism—a single bit of information. Local Realism shows that a single quantum mechanical bit of information, a "qubit," cannot always be localized in a space-time box. This fact provides the fundamental basis of quantum information theory and quantum cryptography. Caltech's quantum science and technology program, the 2019 $1.28-billion U.S. National Quantum Initiative, and the 2019 $400 million Israeli National Quantum Initiative all rely on the reality of entanglement. The Chinese Micius quantum-encrypted communications satellite system's configuration is almost identical to that of the Freedman–Clauser experiment. It uses the CHSH inequality to verify entanglement's persistence through outer space.

## Can you tell us more about your family's strong connection with Caltech?

My dad, Francis H. Clauser [BS '34, MS '35, PhD '37, Distinguished Alumni Award '66] and his brother Milton U. Clauser [BS '34, MS '35, PhD '37] were PhD students at Caltech under Theodore von Kármán . Francis Clauser was Clark Blanchard Millikan Professor of Engineering at Caltech (Distinguished Faculty Award '80) and chair of Caltech's Division of Engineering and Applied Science. Milton U. Clauser's son, Milton J. Clauser [PhD '66], and grandson, Karl Clauser [BS '86] both went to Caltech. My mom, Catharine McMillan Clauser was Caltech's humanities librarian, where she met my dad. Her brother, Edwin McMillan [BS '28, MS '29], is a Caltech alum and '51 Nobel Laureate. The family now maintains Caltech's "Milton and Francis Doctoral Prize" awarded at Caltech commencements.

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## Nobel Prize : Quantum Entanglement Unveiled

7 October 2022: We have replaced our initial one-paragraph announcement with a full-length Focus story.

The Nobel Prize in Physics this year recognizes efforts to take quantum weirdness out of philosophy discussions and to place it on experimental display for all to see. The award is shared by Alain Aspect, John Clauser, and Anton Zeilinger, all of whom showed a mastery of entanglement—a quantum relationship between two particles that can exist over long distances. Using entangled photons, Clauser and Aspect performed some of the first “Bell tests,” which confirmed quantum mechanics predictions while putting to bed certain alternative theories based on classical physics. Zeilinger used some of those Bell-test techniques to demonstrate entanglement control methods that can be applied to quantum computing, quantum cryptography, and other quantum information technologies.

Since its inception, quantum mechanics has been wildly successful at predicting the outcomes of experiments. But the theory assumes that some properties of a particle are inherently uncertain—a fact that bothered many physicists, including Albert Einstein. He and his colleagues expressed their concern in a paradox they described in 1935 [ 1 ]: Imagine creating two quantum mechanically entangled particles and distributing them between two separated researchers, characters later named Alice and Bob. If Alice measures her particle, then she learns something about Bob’s particle—as if her measurement instantaneously changed the uncertainty about the state of his particle. To avoid such “spooky action at a distance,” Einstein proposed that lying underneath the quantum framework is a set of classical “hidden variables” that determine precisely how a particle will behave, rather than providing only probabilities.

The hidden variables were unmeasurable—by definition—so most physicists deemed their existence to be a philosophical issue, not an experimental one. That changed in 1964 when John Bell of the University of Wisconsin-Madison, proposed a thought experiment that could directly test the hidden variable hypothesis [ 2 ]. As in Einstein’s paradox, Alice and Bob are each sent one particle of an entangled pair. This time, however, the two researchers measure their respective particles in different ways and compare their results. Bell showed that if hidden variables exist, the experimental results would obey a mathematical inequality. However, if quantum mechanics was correct, the inequality would be violated.

Bell’s work showed how to settle the debate between quantum and classical views, but his proposed experiment assumed detector capabilities that weren’t feasible. A revised version using photons and polarizers was proposed in 1969 by Clauser, then at Columbia University, along with his colleagues [ 3 ]. Three years later, Clauser and Stuart Freedman (both at the University of California, Berkeley) succeeded in performing that experiment [ 4 ].

The Freedman-Clauser experiment used entangled photons obtained by exciting calcium atoms. When a calcium atom de-excites, it can emit two photons whose polarizations are aligned. The researchers installed two detectors (Alice and Bob) on opposite sides of the calcium source and measured the rate of coincidences—two photons hitting the detectors simultaneously. Each detector was equipped with a polarizer that could be rotated to an arbitrary orientation.

Freedman and Clauser showed theoretically that quantum mechanics predictions diverge strongly from hidden variable predictions when Alice and Bob’s polarizers are offset from each other by 22.5° or 67.5°. The researchers collected 200 hours of data and found that the coincidence rates violated a revamped Bell’s inequality, proving that quantum mechanics is right.

The results of the first Bell test were a blow to hidden variables, but there were “loopholes” that hidden-variable supporters could claim to rescue their theory. One of the most significant loopholes was based on the idea that the setting of Alice’s polarizer could have some influence on Bob’s polarizer or on the photons that are created at the source. Such effects could allow the elements of a hidden-variable system to “conspire” together to produce measurement outcomes that mimic quantum mechanics.

To close this so-called locality loophole, Aspect and his colleagues at the Institute of Optics Graduate School in France performed an updated Bell test in 1982, using an innovative method for randomly changing the polarizer orientations [ 5 ]. The system worked like a railroad switch, rapidly diverting photons between two separate “tracks,” each with a different polarizer. The changes were made as the photons were traveling from the source to the detectors, so there was not enough time for coordination between supposed hidden variables.

Zeilinger, who is now at the University of Vienna, has also worked on removing loopholes from Bell tests (see Viewpoint: Closing the Door on Einstein and Bohr’s Quantum Debate , written by Aspect). In 2017, for example, he and his collaborators devised a way to use light from distant stars as a random input for setting polarizer orientations (see Synopsis: Cosmic Test of Quantum Mechanics ).

Zeilinger also used the techniques of entanglement control to explore practical applications, such as quantum teleportation and entanglement swapping. For the latter, he and his team showed in 1998 that they could create entanglement between two photons that were never in contact [ 6 ]. In this experiment, two sets of entangled photon pairs are generated at two separate locations. One from each pair is sent to Alice and Bob, while the other two photons are sent to a third person, Cecilia. Cecilia performs a Bell-like test on her two photons, and when she records a particular result, Alice’s photon winds up being entangled with Bob's. This swapping could be used to send entanglement over longer distances than is currently possible with optical fibers (see Research News: The Key Device Needed for a Quantum Internet ).

“Quantum entanglement is not questioned anymore,” says quantum physicist Jean Dalibard from the College of France. “It has become a tool, in particular in the emerging field of quantum information processing, and the three nominated scientists can be considered as the godfathers of this new domain.”

Quantum information specialist Jian-Wei Pan of the University of Science and Technology of China in Hefei says the winners are fully deserving of the prize. He has worked with Zeilinger on several projects, including a quantum-based satellite link (see Focus: Intercontinental, Quantum-Encrypted Messaging and Video ). “Now, in China, we are putting a lot of effort into actually turning these dreams into reality, hoping to make the quantum technologies practically useful for our society.”

–Michael Schirber

Michael Schirber is a Corresponding Editor for Physics Magazine based in Lyon, France.

- A. Einstein et al. , “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47 , 777 (1935) .
- J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1 , 195 (1964) .
- J. F. Clauser et al. , “Proposed experiment to test local hidden-variable theories,” Phys. Rev. Lett. 23 , 880 (1969) .
- S. J. Freedman and J. F. Clauser, “Experimental test of local hidden-variable theories,” Phys. Rev. Lett. 28 , 938 (1972) .
- A. Aspect et al. , “Experimental test of Bell’s inequalities using time-varying analyzers,” Phys. Rev. Lett. 49 , 1804 (1982) .
- J. W. Pan et al. , “Experimental entanglement swapping: Entangling photons that never interacted,” Phys. Rev. Lett. 80 , 3891 (1998) .

## More Information

Research News: Hiding Secrets Using Quantum Entanglement

Research News: Diagramming Quantum Weirdness

APS press release

The Nobel Prize in Physics 2022 (Nobel Foundation)

## Experimental Test of Bell's Inequalities Using Time-Varying Analyzers

Alain Aspect, Jean Dalibard, and Gérard Roger

Phys. Rev. Lett. 49 , 1804 (1982)

Published December 20, 1982

## Experimental Entanglement Swapping: Entangling Photons That Never Interacted

Jian-Wei Pan, Dik Bouwmeester, Harald Weinfurter, and Anton Zeilinger

Phys. Rev. Lett. 80 , 3891 (1998)

Published May 4, 1998

## Experimental Test of Local Hidden-Variable Theories

Stuart J. Freedman and John F. Clauser

Phys. Rev. Lett. 28 , 938 (1972)

Published April 3, 1972

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## Science News Explores

Experiments on ‘entangled’ quantum particles won the physics nobel prize.

Physicists Alain Aspect, John Clauser and Anton Zeilinger share the award

Experiments on entanglement — a strange feature of quantum physics — have netted three scientists the 2022 Nobel Prize in physics. When two particles are entangled (illustrated), what happens to one determines what happens to the other — even when the second one is far away.

Nicolle R. Fuller/NSF

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October 5, 2022 at 10:23 am

For their tests of quantum weirdness and its real-world uses, three scientists will share the 2022 Nobel Prize in physics.

Quantum physics is the science of super small things. It governs how atoms and even tinier particles behave. Such itty-bitty bits of matter don’t obey the same rules as larger objects. One especially strange feature of quantum physics is “entanglement.” When two particles are entangled, everything about them — from their speed to the way they spin — is perfectly connected. If you know the state of one particle, then you know the state of the other. This is true even when the linked particles are very far apart.

When this idea was first proposed, physicists like Albert Einstein were skeptical. Math might allow entanglement in theory, they thought. But there should be no way such linked particles could exist in the real world.

This year’s Nobel Prize winners show that, in fact, it does. And it could lead to many new technologies. Completely secure systems of communication, for instance. Or quantum computers that solve problems that stump any ordinary computer.

Each of this year’s winners will take home a third of the prize money, which totals 10 million Swedish kronor (worth roughly $900,000).

One winner is Alain Aspect. He works at the Université Paris-Saclay and École Polytechnique in France. Another is John Clauser, who runs a company in California. These two confirmed that the rules of quantum physics really do rule the world.

Anton Zeilinger, the third winner, works at the University of Vienna in Austria. He has taken advantage of the quantum strangeness confirmed by Aspect and Clauser to develop new technologies.

“Today, we honor three physicists whose pioneering experiments showed us that the strange world of entanglement … is not just the micro-world of atoms, and certainly not the virtual world of science fiction or mysticism,” said Thors Hans Hansson. “It’s the real world that we all live in.” Hansson is a member of the Nobel Committee for Physics, which chose the winners. He spoke at an October 4 press conference at the Royal Swedish Academy of Sciences in Stockholm. It’s where the award was announced.

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“It was certainly very exciting to learn about the three laureates,” says Jerry Chow. He’s a physicist at IBM Quantum in Yorktown Heights, N.Y. “They’re all very, very well known in our quantum community. And their work is something that’s really been a big part of many people’s research efforts over many years.”

## Proving entanglement

The discovery that quantum rules govern tiny things like atoms and electrons shook up early 20th century physics. Many leading scientists, such as Einstein, thought the math of quantum physics worked in theory . But they weren’t sure it could truly describe the real world. Ideas like entanglement were just too weird. How could you really know the state of one particle by looking at another?

Einstein suspected the quantum weirdness of entanglement was an illusion. There must be some classical physics that could explain how it worked — like the secret to a magic trick. Lab tests, he suspected, were just too crude to uncover that hidden information.

Other scientists believed there was no secret to entanglement. Quantum particles had no hidden back channels for sending information. Some particles could just become perfectly linked, and that was that. It was the way the world worked.

In the 1960s, physicist John Bell came up with a test to prove there was no hidden communication between quantum objects. Clauser was the first one to develop an experiment to run this test. His results supported Bell’s idea about entanglement. Linked particles just are .

But Clauser’s test had some loopholes. These left room for doubt. Aspect ran another test that ruled out any chance quantum strangeness could be cleared up by some hidden explanation.

Clauser and Aspect’s experiments involved pairs of light particles, or photons . They created pairs of entangled photons. This meant the particles acted like a single object. As the photons moved apart, they stayed entangled. That is, they kept acting as a single, extended object. Measuring the features of one instantly revealed those of the other. This was true no matter how far apart the photons got.

Entanglement is fragile and hard to maintain. But Clauser and Aspect’s work showed that quantum effects could not be explained by classical physics.

Zeilinger’s experiments show the practical uses of these effects. For instance, he has used entanglement to create absolutely secure encryption and communication. Here’s how it works: Interacting with one entangled particle affects another. So, anyone trying to peek at secret quantum information would break the particles’ entanglement as soon as they snooped. That means nobody can spy on a quantum message without getting caught.

Zeilinger has also pioneered another use for entanglement. That is quantum teleportation . This isn’t like people popping from one place to another in science fiction and fantasy. The effect involves sending information from one place to another about a quantum object.

Quantum computers are another technology that would rely on entangled particles. Normal computers process data using ones and zeroes. Quantum computers would use bits of information that are each a blend of one and zero. In theory, such machines could run calculations that no normal computer can.

## Quantum boom

“This [award] is a very nice and positive surprise to me,” says Nicolas Gisin. He’s a physicist at the University of Geneva in Switzerland. “This prize is very well-deserved. But comes a bit late. Most of that work was done in the [1970s and 1980s]. But the Nobel Committee was very slow and now is rushing after the boom of quantum technologies.”

That boom is happening around the world, Gisin says. “Instead of having a few individuals pioneering the field, now we have really huge crowds of physicists and engineers that work together.”

Some of the most cutting-edge uses of quantum physics are still in their infancy. But the three new Nobel laureates have helped transform this strange science from an abstract curiosity into something useful. Their work validates some key, once-contested ideas of modern physics. Someday, it may also become a basic part of our daily lives, in ways not even Einstein could deny.

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## What is quantum entanglement? A physicist explains the science of Einstein’s ‘spooky action at a distance’

Associate Professor of Physics, University of South Florida

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The 2022 Nobel Prize in physics recognized three scientists who made groundbreaking contributions in understanding one of the most mysterious of all natural phenomena: quantum entanglement.

In the simplest terms, quantum entanglement means that aspects of one particle of an entangled pair depend on aspects of the other particle, no matter how far apart they are or what lies between them. These particles could be, for example, electrons or photons, and an aspect could be the state it is in, such as whether it is “spinning” in one direction or another.

The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe . Albert Einstein famously called the phenomenon “spooky action at a distance.”

Having spent the better part of two decades conducting experiments rooted in quantum mechanics , I have come to accept its strangeness. Thanks to ever more precise and reliable instruments and the work of this year’s Nobel winners, Alain Aspect , John Clauser and Anton Zeilinger , physicists now integrate quantum phenomena into their knowledge of the world with an exceptional degree of certainty.

However, even until the 1970s, researchers were still divided over whether quantum entanglement was a real phenomenon. And for good reasons – who would dare contradict the great Einstein, who himself doubted it? It took the development of new experimental technology and bold researchers to finally put this mystery to rest.

## Existing in multiple states at once

To truly understand the spookiness of quantum entanglement, it is important to first understand quantum superposition . Quantum superposition is the idea that particles exist in multiple states at once. When a measurement is performed, it is as if the particle selects one of the states in the superposition.

For example, many particles have an attribute called spin that is measured either as “up” or “down” for a given orientation of the analyzer. But until you measure the spin of a particle, it simultaneously exists in a superposition of spin up and spin down.

There is a probability attached to each state, and it is possible to predict the average outcome from many measurements. The likelihood of a single measurement being up or down depends on these probabilities, but is itself unpredictable .

Though very weird, the mathematics and a vast number of experiments have shown that quantum mechanics correctly describes physical reality.

## Two entangled particles

The spookiness of quantum entanglement emerges from the reality of quantum superposition, and was clear to the founding fathers of quantum mechanics who developed the theory in the 1920s and 1930s.

To create entangled particles you essentially break a system into two, where the sum of the parts is known. For example, you can split a particle with spin of zero into two particles that necessarily will have opposite spins so that their sum is zero.

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper that describes a thought experiment designed to illustrate a seeming absurdity of quantum entanglement that challenged a foundational law of the universe.

A simplified version of this thought experiment , attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin “collapse” into either up or down – instantaneously collapsing the other particle into the opposite spin. This seems to suggest that the particles communicate with each other through some means that moves faster than the speed of light. But according to the laws of physics, nothing can travel faster than the speed of light. Surely the measured state of one particle cannot instantaneously determine the state of another particle at the far end of the universe?

Physicists, including Einstein, proposed a number of alternative interpretations of quantum entanglement in the 1930s. They theorized there was some unknown property – dubbed hidden variables – that determined the state of a particle before measurement . But at the time, physicists did not have the technology nor a definition of a clear measurement that could test whether quantum theory needed to be modified to include hidden variables.

## Disproving a theory

It took until the 1960s before there were any clues to an answer. John Bell, a brilliant Irish physicist who did not live to receive the Nobel Prize, devised a scheme to test whether the notion of hidden variables made sense.

Bell produced an equation now known as Bell’s inequality that is always correct – and only correct – for hidden variable theories, and not always for quantum mechanics. Thus, if Bell’s equation was found not to be satisfied in a real-world experiment, local hidden variable theories can be ruled out as an explanation for quantum entanglement.

The experiments of the 2022 Nobel laureates, particularly those of Alain Aspect , were the first tests of the Bell inequality . The experiments used entangled photons, rather than pairs of an electron and a positron, as in many thought experiments. The results conclusively ruled out the existence of hidden variables, a mysterious attribute that would predetermine the states of entangled particles. Collectively, these and many follow-up experiments have vindicated quantum mechanics. Objects can be correlated over large distances in ways that physics before quantum mechanics can not explain.

Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication . The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light.

Today, physicists continue to research quantum entanglement and investigate potential practical applications . Although quantum mechanics can predict the probability of a measurement with incredible accuracy, many researchers remain skeptical that it provides a complete description of reality. One thing is certain, though. Much remains to be said about the mysterious world of quantum mechanics.

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## Light from ancient quasars helps confirm quantum entanglement

Results are among the strongest evidence yet for “spooky action at a distance.”.

Last year, physicists at MIT, the University of Vienna, and elsewhere provided strong support for quantum entanglement, the seemingly far-out idea that two particles, no matter how distant from each other in space and time, can be inextricably linked, in a way that defies the rules of classical physics.

Take, for instance, two particles sitting on opposite edges of the universe. If they are truly entangled, then according to the theory of quantum mechanics their physical properties should be related in such a way that any measurement made on one particle should instantly convey information about any future measurement outcome of the other particle — correlations that Einstein skeptically saw as “spooky action at a distance.”

In the 1960s, the physicist John Bell calculated a theoretical limit beyond which such correlations must have a quantum, rather than a classical, explanation.

But what if such correlations were the result not of quantum entanglement, but of some other hidden, classical explanation? Such “what-ifs” are known to physicists as loopholes to tests of Bell’s inequality, the most stubborn of which is the “freedom-of-choice” loophole: the possibility that some hidden, classical variable may influence the measurement that an experimenter chooses to perform on an entangled particle, making the outcome look quantumly correlated when in fact it isn’t.

Last February, the MIT team and their colleagues significantly constrained the freedom-of-choice loophole, by using 600-year-old starlight to decide what properties of two entangled photons to measure. Their experiment proved that, if a classical mechanism caused the correlations they observed, it would have to have been set in motion more than 600 years ago, before the stars’ light was first emitted and long before the actual experiment was even conceived.

Now, in a paper published today in Physical Review Letters , the same team has vastly extended the case for quantum entanglement and further restricted the options for the freedom-of-choice loophole. The researchers used distant quasars, one of which emitted its light 7.8 billion years ago and the other 12.2 billion years ago, to determine the measurements to be made on pairs of entangled photons. They found correlations among more than 30,000 pairs of photons, to a degree that far exceeded the limit that Bell originally calculated for a classically based mechanism.

“If some conspiracy is happening to simulate quantum mechanics by a mechanism that is actually classical, that mechanism would have had to begin its operations — somehow knowing exactly when, where, and how this experiment was going to be done — at least 7.8 billion years ago. That seems incredibly implausible, so we have very strong evidence that quantum mechanics is the right explanation,” says co-author Alan Guth , the Victor F. Weisskopf Professor of Physics at MIT.

“The Earth is about 4.5 billion years old, so any alternative mechanism — different from quantum mechanics — that might have produced our results by exploiting this loophole would’ve had to be in place long before even there was a planet Earth, let alone an MIT,” adds David Kaiser , the Germeshausen Professor of the History of Science and professor of physics at MIT. “So we’ve pushed any alternative explanations back to very early in cosmic history.”

Guth and Kaiser’s co-authors include Anton Zeilinger and members of his group at the Austrian Academy of Sciences and the University of Vienna, as well as physicists at Harvey Mudd College and the University of California at San Diego.

A decision, made billions of years ago

In 2014, Kaiser and two members of the current team, Jason Gallicchio and Andrew Friedman, proposed an experiment to produce entangled photons on Earth — a process that is fairly standard in studies of quantum mechanics. They planned to shoot each member of the entangled pair in opposite directions, toward light detectors that would also make a measurement of each photon using a polarizer. Researchers would measure the polarization, or orientation, of each incoming photon’s electric field, by setting the polarizer at various angles and observing whether the photons passed through — an outcome for each photon that researchers could compare to determine whether the particles showed the hallmark correlations predicted by quantum mechanics.

The team added a unique step to the proposed experiment, which was to use light from ancient, distant astronomical sources, such as stars and quasars, to determine the angle at which to set each respective polarizer. As each entangled photon was in flight, heading toward its detector at the speed of light, researchers would use a telescope located at each detector site to measure the wavelength of a quasar’s incoming light. If that light was redder than some reference wavelength, the polarizer would tilt at a certain angle to make a specific measurement of the incoming entangled photon — a measurement choice that was determined by the quasar. If the quasar’s light was bluer than the reference wavelength, the polarizer would tilt at a different angle, performing a different measurement of the entangled photon.

In their previous experiment, the team used small backyard telescopes to measure the light from stars as close as 600 light years away. In their new study, the researchers used much larger, more powerful telescopes to catch the incoming light from even more ancient, distant astrophysical sources: quasars whose light has been traveling toward the Earth for at least 7.8 billion years — objects that are incredibly far away and yet are so luminous that their light can be observed from Earth.

Tricky timing

On Jan. 11, 2018, “the clock had just ticked past midnight local time,” as Kaiser recalls, when about a dozen members of the team gathered on a mountaintop in the Canary Islands and began collecting data from two large, 4-meter-wide telescopes: the William Herschel Telescope and the Telescopio Nazionale Galileo, both situated on the same mountain and separated by about a kilometer.

One telescope focused on a particular quasar, while the other telescope looked at another quasar in a different patch of the night sky. Meanwhile, researchers at a station located between the two telescopes created pairs of entangled photons and beamed particles from each pair in opposite directions toward each telescope.

In the fraction of a second before each entangled photon reached its detector, the instrumentation determined whether a single photon arriving from the quasar was more red or blue, a measurement that then automatically adjusted the angle of a polarizer that ultimately received and detected the incoming entangled photon.

“The timing is very tricky,” Kaiser says. “Everything has to happen within very tight windows, updating every microsecond or so.”

Demystifying a mirage

The researchers ran their experiment twice, each for around 15 minutes and with two different pairs of quasars. For each run, they measured 17,663 and 12,420 pairs of entangled photons, respectively. Within hours of closing the telescope domes and looking through preliminary data, the team could tell there were strong correlations among the photon pairs, beyond the limit that Bell calculated, indicating that the photons were correlated in a quantum-mechanical manner.

Guth led a more detailed analysis to calculate the chance, however slight, that a classical mechanism might have produced the correlations the team observed.

He calculated that, for the best of the two runs, the probability that a mechanism based on classical physics could have achieved the observed correlation was about 10 to the minus 20 — that is, about one part in one hundred billion billion, “outrageously small,” Guth says. For comparison, researchers have estimated the probability that the discovery of the Higgs boson was just a chance fluke to be about one in a billion.

“We certainly made it unbelievably implausible that a local realistic theory could be underlying the physics of the universe,” Guth says.

And yet, there is still a small opening for the freedom-of-choice loophole. To limit it even further, the team is entertaining ideas of looking even further back in time, to use sources such as cosmic microwave background photons that were emitted as leftover radiation immediately following the Big Bang, though such experiments would present a host of new technical challenges.

“It is fun to think about new types of experiments we can design in the future, but for now, we are very pleased that we were able to address this particular loophole so dramatically. Our experiment with quasars puts extremely tight constraints on various alternatives to quantum mechanics. As strange as quantum mechanics may seem, it continues to match every experimental test we can devise,” Kaiser says.

This research was supported in part by the Austrian Academy of Sciences, the Austrian Science Fund, the U.S. National Science Foundation, and the U.S. Department of Energy.

- Paper: “Cosmic Bell Test Using Random Measurement Settings from High-Redshift Quasars”

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Collaboration Site | Physics Results

## ATLAS achieves highest-energy detection of quantum entanglement

28 September 2023 | By

Quantum entanglement is one of the most astonishing properties of quantum mechanics. If two particles are entangled, the state of one particle cannot be described independently from the other. This is a unique property of the quantum world and forms a crucial difference between classical and quantum theories of physics. It is so important, the 2022 Nobel Prize in Physics was awarded to Alain Aspect, John F. Clauser and Anton Zeilinger "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science".

The large mass of the top quark, which is greater than any other particle, remains one of the most enduring mysteries of the Standard Model. Why this is so remains unexplained, however, the top quark has many unique properties to exploit as a result. The top quark is so heavy that it is extremely unstable and decays before it has time to hadronise, transferring all of its quantum numbers to its decay particles. Physicists can detect these decay particles and thus reconstruct the quantum state of a top quark, a feat that is impossible with any other quark. Most importantly, they can measure its spin and use it to show that entanglement can be studied in top-quark-pair production at the LHC .

Entanglement has indeed been measured in the past, but not quite like this. Most previous entanglement measurements involved low non-relativistic energies, typically utilising photons or electrons. The LHC collides protons with an incredibly high centre-of-mass energy. The data used in ATLAS’ new measurement were obtained from collisions at 13 TeV collected between 2015 and 2018. This means researchers are delving into an energy scale over 12 orders of magnitude (a thousand billion times) higher than typical laboratory experiments.

## This is the first-ever observation of quantum entanglement between a pair of quarks and the highest-energy measurement of entanglement.

In a new result from the ATLAS Collaboration, physicists studied the effects of entanglement in top quarks. They looked at top-quark pairs at their “production threshold”, i.e. when the invariant mass of the pair is at its minimum (approximately twice the mass of the top quark) and the top quarks are expected to be maximally entangled.

The degree of entanglement (D) is related to the angular distribution of the particles the top quarks decay into – giving physicists a direct way to study this quantum effect. Researchers measured the angular separation of the top-quarks’ decay products (in the rest frames of the top quarks), correcting for detector effects that may impact its measured value. As a result, they calculated D at the particle level to be –0.547 ± 0.021. The result is significantly lower than the minimum value indicative of a non-entangled state, and more than passes the five standard deviation threshold required for an observation of the entanglement of top-quark pairs (see Figure 1).

This is the first-ever observation of entanglement between a pair of quarks and the highest-energy measurement of entanglement. Apart from the fundamental interest of testing quantum entanglement in a new environment, this measurement paves the way to use the LHC as a laboratory to study quantum information and other foundational problems in quantum mechanics.

About the banner image : Artistic visualisation of top-quark entanglement. The line between the particles emphasises the non-separability of the top-quark pair, which is produced by LHC collisions and recorded by ATLAS. (Image: Daniel Dominguez/CERN)

- Observation of quantum entanglement in top quark pair production using pp collisions of 13 TeV with the ATLAS detector (ATLAS-CONF-2023-069)
- TOP2023 presentation by Yoav Afik: Spin and entanglement ATLAS
- Afik, Y., de Nova, J.R.M., Entanglement and quantum tomography with top quarks at the LHC (Eur. Phys. J. Plus 136, 907 (2021))
- Highest-energy observation of quantum entanglement , CERN Courier , 29 September 2023

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## What is quantum entanglement? A physicist explains Einstein’s ‘spooky action at a distance’

The 2022 Nobel Prize in physics recognized three scientists who made groundbreaking contributions in understanding one of the most mysterious of all natural phenomena: quantum entanglement.

In the simplest terms, quantum entanglement means that aspects of one particle of an entangled pair depend on aspects of the other particle, no matter how far apart they are or what lies between them. These particles could be, for example, electrons or photons, and an aspect could be the state it is in, such as whether it is “spinning” in one direction or another.

The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe . Albert Einstein famously called the phenomenon “spooky action at a distance.”

Having spent the better part of two decades conducting experiments rooted in quantum mechanics , I have come to accept its strangeness. Thanks to ever more precise and reliable instruments and the work of this year’s Nobel winners, Alain Aspect , John Clauser and Anton Zeilinger , physicists now integrate quantum phenomena into their knowledge of the world with an exceptional degree of certainty.

However, even until the 1970s, researchers were still divided over whether quantum entanglement was a real phenomenon. And for good reasons – who would dare contradict the great Einstein, who himself doubted it? It took the development of new experimental technology and bold researchers to finally put this mystery to rest.

## Existing in multiple states at once

To truly understand the spookiness of quantum entanglement, it is important to first understand quantum superposition . Quantum superposition is the idea that particles exist in multiple states at once. When a measurement is performed, it is as if the particle selects one of the states in the superposition.

For example, many particles have an attribute called spin that is measured either as “up” or “down” for a given orientation of the analyzer. But until you measure the spin of a particle, it simultaneously exists in a superposition of spin up and spin down.

There is a probability attached to each state, and it is possible to predict the average outcome from many measurements. The likelihood of a single measurement being up or down depends on these probabilities, but is itself unpredictable .

Though very weird, the mathematics and a vast number of experiments have shown that quantum mechanics correctly describes physical reality.

## Two entangled particles

The spookiness of quantum entanglement emerges from the reality of quantum superposition, and was clear to the founding fathers of quantum mechanics who developed the theory in the 1920s and 1930s.

To create entangled particles you essentially break a system into two, where the sum of the parts is known. For example, you can split a particle with spin of zero into two particles that necessarily will have opposite spins so that their sum is zero.

In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen published a paper that describes a thought experiment designed to illustrate a seeming absurdity of quantum entanglement that challenged a foundational law of the universe.

A simplified version of this thought experiment , attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin “collapse” into either up or down – instantaneously collapsing the other particle into the opposite spin. This seems to suggest that the particles communicate with each other through some means that moves faster than the speed of light. But according to the laws of physics, nothing can travel faster than the speed of light. Surely the measured state of one particle cannot instantaneously determine the state of another particle at the far end of the universe?

Physicists, including Einstein, proposed a number of alternative interpretations of quantum entanglement in the 1930s. They theorized there was some unknown property – dubbed hidden variables – that determined the state of a particle before measurement . But at the time, physicists did not have the technology nor a definition of a clear measurement that could test whether quantum theory needed to be modified to include hidden variables.

## Disproving a theory

It took until the 1960s before there were any clues to an answer. John Bell, a brilliant Irish physicist who did not live to receive the Nobel Prize, devised a scheme to test whether the notion of hidden variables made sense.

Bell produced an equation now known as Bell’s inequality that is always correct – and only correct – for hidden variable theories, and not always for quantum mechanics. Thus, if Bell’s equation was found not to be satisfied in a real-world experiment, local hidden variable theories can be ruled out as an explanation for quantum entanglement.

The experiments of the 2022 Nobel laureates, particularly those of Alain Aspect , were the first tests of the Bell inequality . The experiments used entangled photons, rather than pairs of an electron and a positron, as in many thought experiments. The results conclusively ruled out the existence of hidden variables, a mysterious attribute that would predetermine the states of entangled particles. Collectively, these and many follow-up experiments have vindicated quantum mechanics. Objects can be correlated over large distances in ways that physics before quantum mechanics can not explain.

Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication . The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light.

Today, physicists continue to research quantum entanglement and investigate potential practical applications . Although quantum mechanics can predict the probability of a measurement with incredible accuracy, many researchers remain skeptical that it provides a complete description of reality. One thing is certain, though. Much remains to be said about the mysterious world of quantum mechanics.

Andreas Muller , Associate Professor of Physics, University of South Florida

This article is republished from The Conversation under a Creative Commons license. Read the original article .

## How merging black holes could reveal the nature of dark matter

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## Quantum 'yin-yang' shows two photons being entangled in real-time

The stunning experiment, which reconstructs the properties of entangled photons from a 2D interference pattern, could be used to design faster quantum computers.

Scientists have used a first-of-its-kind technique to visualize two entangled light particles in real time — making them appear as a stunning quantum "yin-yang" symbol.

The new method, called biphoton digital holography, uses an ultra high-precision camera and could be used to massively speed up future quantum measurements.

The researchers published their findings Aug. 14 in the journal Nature Photonics .

Related: Bizarre particle that can remember its own past created inside quantum computer

Quantum entanglement — the weird connection between two far-apart particles that Albert Einstein objected to as "spooky action at a distance" — enables two light particles, or photons, to become inextricably bound to each other, so that a change to one causes a change in the other, no matter how far apart they are.

To make accurate predictions about a quantum object, physicists need to find its wavefunction: a description of its state existing in a superposition of all the possible physical values a photon can take. Entanglement makes finding the wavefunction of two connected particles a challenge, as any measurement of one also causes an instantaneous change in the other.

Physicists usually approach this hurdle through a method known as quantum tomography. By taking a complex quantum state and applying a projection to it, they measure some property belonging to that state, such as its polarization or momentum, in isolation from others.

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By repeating these measurements on multiple copies of the quantum state, physicists can build up a sense of the original from lower-dimensional slices — like reconstructing the shape of a 3D object from the 2D shadows it casts on surrounding walls.

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This process gives all the right information, but it also requires a lot of measurements and spits out plentiful "disallowed" states that don't follow the laws of physics to boot. This leaves scientists with the onerous task of painstakingly weeding out nonsensical, unphysical states, an effort that can take hours or even days depending on a system's complexity.

To get around this, the researchers used holography to encode information from higher dimensions into manageable, lower-dimensional chunks.

Optical holograms use two light beams to create a 3D image: one beam hits the object and bounces off of it, while the other shines on a recording medium. The hologram forms from the pattern of light interference, or the pattern in which the peaks and troughs of the two light waves add up or cancel each other out. The physicists used a similar method to capture an image of the entangled photon state through the interference pattern they made with another known state. Then, by capturing the resulting image with a nanosecond precise camera, the researchers teased apart the interference pattern they received — revealing a stunning yin-yang image of the two entangled photons.

"This method is exponentially faster than previous techniques, requiring only minutes or seconds instead of days," study co-author Alessio D'Errico , a postdoctoral fellow at the University of Ottawa in Canada, said in a statement .

Ben Turner is a U.K. based staff writer at Live Science. He covers physics and astronomy, among other topics like tech and climate change. He graduated from University College London with a degree in particle physics before training as a journalist. When he's not writing, Ben enjoys reading literature, playing the guitar and embarrassing himself with chess.

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## What Is Entanglement and Why Is It Important?

Entanglement is at the heart of quantum physics and future quantum technologies. Like other aspects of quantum science, the phenomenon of entanglement reveals itself at very tiny, subatomic scales. When two particles, such as a pair of photons or electrons, become entangled, they remain connected even when separated by vast distances. In the same way that a ballet or tango emerges from individual dancers, entanglement arises from the connection between particles. It is what scientists call an emergent property.

## How do scientists explain quantum entanglement?

In the video below, Caltech faculty members take a stab at explaining entanglement. Featured: Rana Adhikari, professor of physics; Xie Chen, professor of theoretical physics; Manuel Endres, professor of physics and Rosenberg Scholar; and John Preskill, Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter.

## Unbreakable Correlation

When researchers study entanglement , they often use a special kind of crystal to generate two entangled particles from one. The entangled particles are then sent off to different locations. For this example, let's say the researchers want to measure the direction the particles are spinning, which can be either up or down along a given axis. Before the particles are measured, each will be in a state of superposition , or both "spin up" and "spin down" at the same time.

If the researcher measures the direction of one particle's spin and then repeats the measurement on its distant, entangled partner, that researcher will always find that the pair are correlated: if one particle's spin is up, the other's will be down (the spins may instead both be up or both be down, depending on how the experiment is designed, but there will always be a correlation). Returning to our dancer metaphor, this would be like observing one dancer and finding them in a pirouette, and then automatically knowing the other dancer must also be performing a pirouette. The beauty of entanglement is that just knowing the state of one particle automatically tells you something about its companion, even when they are far apart.

## Are particles really connected across space?

But are the particles really somehow tethered to each other across space, or is something else going on? Some scientists, including Albert Einstein in the 1930s, pointed out that the entangled particles might have always been spin up or spin down, but that this information was hidden from us until the measurements were made. Such "local hidden variable theories" argued against the mind-boggling aspect of entanglement, instead proposing that something more mundane, yet unseen, is going on.

Thanks to theoretical work by John Stewart Bell in the 1960s, and experimental work done by Caltech alumnus John Clauser (BS '64) and others beginning in the 1970s, scientists have ruled out these local hidden-variable theories. A key to the researchers' success involved observing entangled particles from different angles. In the experiment mentioned above, this means that a researcher would measure their first particle as spin up, but then use a different viewing angle (or a different spin axis direction) to measure the second particle. Rather than the two particles matching up as before, the second particle would have gone back into a state of superposition and, once observed, could be either spin up or down. The choice of the viewing angle changed the outcome of the experiment, which means that there cannot be any hidden information buried inside a particle that determines its spin before it is observed. The dance of entanglement materializes not from any one particle but from the connections between them.

## Relativity Remains Intact

A common misconception about entanglement is that the particles are communicating with each other faster than the speed of light, which would go against Einstein's special theory of relativity. Experiments have shown that this is not true, nor can quantum physics be used to send faster-than-light communications. Though scientists still debate how the seemingly bizarre phenomenon of entanglement arises, they know it is a real principle that passes test after test. In fact, while Einstein famously described entanglement as "spooky action at a distance," today's quantum scientists say there is nothing spooky about it.

"It may be tempting to think that the particles are somehow communicating with each other across these great distances, but that is not the case," says Thomas Vidick , a professor of computing and mathematical sciences at Caltech. "There can be correlation without communication," and the particles "can be thought of as one object."

## Networks of Entanglement

Entanglement can also occur among hundreds, millions, and even more particles. The phenomenon is thought to take place throughout nature, among the atoms and molecules in living species and within metals and other materials. When hundreds of particles become entangled, they still act as one unified object. Like a flock of birds, the particles become a whole entity unto itself without being in direct contact with one another. Caltech scientists focus on the study of these so-called many-body entangled systems, both to understand the fundamental physics and to create and develop new quantum technologies. As John Preskill, Caltech's Richard P. Feynman Professor of Theoretical Physics, Allen V. C. Davis and Lenabelle Davis Leadership Chair, and director of the Institute for Quantum Information and Matter, says, "We are making investments in and betting on entanglement being one of the most important themes of 21st-century science."

## Dive Deeper

## Physicists ‘entangle’ individual molecules for the first time, bringing about a new platform for quantum science

Laser setup for cooling, controlling, and entangling individual molecules.

In a noteworthy first, a team of Princeton physicists has been able to link together individual molecules into special states that are quantum mechanically “entangled.” In these bizarre states, the molecules remain correlated with each other — and can interact simultaneously — even if they are miles apart, or indeed, even if they occupy opposite ends of the universe. This research was published in the current issue of the journal Science .

Members of the Princeton research team. From left to right, Assistant Professor of Physics Lawrence Cheuk, graduate student in electrical engineering Yukai Lu, and graduate student in physics Connor Holland.

“This is a breakthrough in the world of molecules because of the fundamental importance of quantum entanglement,” said Lawrence Cheuk , an assistant professor of physics at Princeton University, the senior author of the paper and a graduate of Princeton's Class of 2010. “But it is also a breakthrough for practical applications because entangled molecules can be the building blocks for many future applications.”

These include, for example, quantum computers that can solve certain problems much faster than conventional computers, quantum simulators that can model complex materials whose behaviors are difficult to model, and quantum sensors that can measure faster than their traditional counterparts.

“One of the motivations in doing quantum science is that in the practical world it turns out that if you harness the laws of quantum mechanics, you can do a lot better in many areas,” said Connor Holland, a graduate student in the physics department and a co-author on the work.

The ability of quantum devices to outperform classical ones is known as “quantum advantage.” And at the core of quantum advantage are the principles of superposition and quantum entanglement. While a classical computer bit can assume the value of either 0 or 1, quantum bits, called qubits, can simultaneously be in a superposition of 0 and 1.

The latter concept, entanglement, is a major cornerstone of quantum mechanics. It occurs when two particles become inextricably linked with each other so that this link persists, even if one particle is light-years away from the other particle. It is the phenomenon that Albert Einstein, who at first questioned its validity, described as “spooky action at a distance.” Since then, physicists have demonstrated that entanglement is, in fact, an accurate description of the physical world and how reality is structured.

“Quantum entanglement is a fundamental concept,” said Cheuk, “but it is also the key ingredient that bestows quantum advantage.”

But building quantum advantage and achieving controllable quantum entanglement remain a challenge, not least because engineers and scientists are still unclear about which physical platform is best for creating qubits. In the past decades, many different technologies — such as trapped ions, photons, superconducting circuits, to name only a few — have been explored as candidates for quantum computers and devices. The optimal quantum system or qubit platform could very well depend on the specific application.

Until this experiment, however, molecules had long defied controllable quantum entanglement. But Cheuk and his colleagues found a way, through careful manipulation in the laboratory, to control individual molecules and coax them into these interlocking quantum states. They also believed that molecules have certain advantages — over atoms, for example — that made them especially well-suited for certain applications in quantum information processing and quantum simulation of complex materials. Compared to atoms, for example, molecules have more quantum degrees of freedom and can interact in new ways.

“What this means, in practical terms, is that there are new ways of storing and processing quantum information,” said Yukai Lu, a graduate student in electrical and computer engineering and a co-author of the paper. “For example, a molecule can vibrate and rotate in multiple modes. So, you can use two of these modes to encode a qubit. If the molecular species is polar, two molecules can interact even when spatially separated.”

Nonetheless, molecules have proven notoriously difficult to control in the laboratory because of their complexity. The very degrees of freedom that make them attractive also make them hard to control, or corral, in laboratory settings. Cheuk and his team addressed many of these challenges through a carefully thought-out experiment involving a sophisticated experimental platform known as a “ tweezer array, ” in which individual molecules were picked up by a complex system of tightly focused laser beams, so-called “optical tweezers.”

“Using molecules for quantum science is a new frontier and our demonstration of on-demand entanglement is a key step in demonstrating that molecules can be used as a viable platform for quantum science,” said Cheuk.

In a separate article published in the same issue of Science , an independent research group led by John Doyle and Kang-Kuen Ni at Harvard University and Wolfgang Ketterle at the Massachusetts Institute of Technology achieved similar results.

“The fact that they got the same results verify the reliability of our results,” Cheuk said. “They also show that molecular tweezer arrays are becoming an exciting new platform for quantum science.”

“ On-Demand Entanglement of Molecules in a Reconfigurable Optical Tweezer Array ,” by Connor M. Holland, Yukai Lu, and Lawrence W. Cheuk was published in Science on December 8, 2023, (DOI: 10.1126/science.adf4272 ). The work was supported by Princeton University, the National Science Foundation (2207518) and the Sloan Foundation (FG-2022-19104).

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## Martonosi sketches a path for a new type of computing .

As new devices move quantum computing closer to practical use, the journal Nature recently asked Princeton computer scientist Margaret Martonosi and two colleagues to assess the state of software needed to exploit this powerful computational approach.

## Princeton scientist makes a leap in quantum computing .

A major hurdle in the ambitious quest to design and construct a radically new kind of quantum computer has been finding a way to manipulate the single electrons that very likely will constitute the new machines' processing components or "qubits."

## Choreographing dance of electrons offers promise in pursuit of quantum computers .

Princeton University engineers Alexei Tyryshkin and Stephen Lyon have choreographed the dance of 100 billion electrons across a silicon crystal — an impressive achievement on its own — and also a stride toward developing the technology for powerful machines known as quantum computers.

## Scientists shed light on the private lives of electrons .

A Princeton University researcher and his international collaborators have used lasers to peek into the complex relationship between a single electron and its environment, a breakthrough that could aid the development of quantum computers.

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## Light from ancient quasars helps confirm quantum entanglement

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Last year, physicists at MIT, the University of Vienna, and elsewhere provided strong support for quantum entanglement, the seemingly far-out idea that two particles, no matter how distant from each other in space and time, can be inextricably linked, in a way that defies the rules of classical physics.

Take, for instance, two particles sitting on opposite edges of the universe. If they are truly entangled, then according to the theory of quantum mechanics their physical properties should be related in such a way that any measurement made on one particle should instantly convey information about any future measurement outcome of the other particle — correlations that Einstein skeptically saw as “spooky action at a distance.”

In the 1960s, the physicist John Bell calculated a theoretical limit beyond which such correlations must have a quantum, rather than a classical, explanation.

But what if such correlations were the result not of quantum entanglement, but of some other hidden, classical explanation? Such “what-ifs” are known to physicists as loopholes to tests of Bell’s inequality, the most stubborn of which is the “freedom-of-choice” loophole: the possibility that some hidden, classical variable may influence the measurement that an experimenter chooses to perform on an entangled particle, making the outcome look quantumly correlated when in fact it isn’t.

Last February, the MIT team and their colleagues significantly constrained the freedom-of-choice loophole, by using 600-year-old starlight to decide what properties of two entangled photons to measure. Their experiment proved that, if a classical mechanism caused the correlations they observed, it would have to have been set in motion more than 600 years ago, before the stars’ light was first emitted and long before the actual experiment was even conceived.

Now, in a paper published today in Physical Review Letters , the same team has vastly extended the case for quantum entanglement and further restricted the options for the freedom-of-choice loophole. The researchers used distant quasars, one of which emitted its light 7.8 billion years ago and the other 12.2 billion years ago, to determine the measurements to be made on pairs of entangled photons. They found correlations among more than 30,000 pairs of photons, to a degree that far exceeded the limit that Bell originally calculated for a classically based mechanism.

“If some conspiracy is happening to simulate quantum mechanics by a mechanism that is actually classical, that mechanism would have had to begin its operations — somehow knowing exactly when, where, and how this experiment was going to be done — at least 7.8 billion years ago. That seems incredibly implausible, so we have very strong evidence that quantum mechanics is the right explanation,” says co-author Alan Guth, the Victor F. Weisskopf Professor of Physics at MIT.

“The Earth is about 4.5 billion years old, so any alternative mechanism — different from quantum mechanics — that might have produced our results by exploiting this loophole would’ve had to be in place long before even there was a planet Earth, let alone an MIT,” adds David Kaiser, the Germeshausen Professor of the History of Science and professor of physics at MIT. “So we’ve pushed any alternative explanations back to very early in cosmic history.”

Guth and Kaiser’s co-authors include Anton Zeilinger and members of his group at the Austrian Academy of Sciences and the University of Vienna, as well as physicists at Harvey Mudd College and the University of California at San Diego.

A decision, made billions of years ago

In 2014, Kaiser and two members of the current team, Jason Gallicchio and Andrew Friedman, proposed an experiment to produce entangled photons on Earth — a process that is fairly standard in studies of quantum mechanics. They planned to shoot each member of the entangled pair in opposite directions, toward light detectors that would also make a measurement of each photon using a polarizer. Researchers would measure the polarization, or orientation, of each incoming photon’s electric field, by setting the polarizer at various angles and observing whether the photons passed through — an outcome for each photon that researchers could compare to determine whether the particles showed the hallmark correlations predicted by quantum mechanics.

The team added a unique step to the proposed experiment, which was to use light from ancient, distant astronomical sources, such as stars and quasars, to determine the angle at which to set each respective polarizer. As each entangled photon was in flight, heading toward its detector at the speed of light, researchers would use a telescope located at each detector site to measure the wavelength of a quasar’s incoming light. If that light was redder than some reference wavelength, the polarizer would tilt at a certain angle to make a specific measurement of the incoming entangled photon — a measurement choice that was determined by the quasar. If the quasar’s light was bluer than the reference wavelength, the polarizer would tilt at a different angle, performing a different measurement of the entangled photon.

In their previous experiment, the team used small backyard telescopes to measure the light from stars as close as 600 light years away. In their new study, the researchers used much larger, more powerful telescopes to catch the incoming light from even more ancient, distant astrophysical sources: quasars whose light has been traveling toward the Earth for at least 7.8 billion years — objects that are incredibly far away and yet are so luminous that their light can be observed from Earth.

Tricky timing

On Jan. 11, 2018, “the clock had just ticked past midnight local time,” as Kaiser recalls, when about a dozen members of the team gathered on a mountaintop in the Canary Islands and began collecting data from two large, 4-meter-wide telescopes: the William Herschel Telescope and the Telescopio Nazionale Galileo, both situated on the same mountain and separated by about a kilometer.

One telescope focused on a particular quasar, while the other telescope looked at another quasar in a different patch of the night sky. Meanwhile, researchers at a station located between the two telescopes created pairs of entangled photons and beamed particles from each pair in opposite directions toward each telescope.

In the fraction of a second before each entangled photon reached its detector, the instrumentation determined whether a single photon arriving from the quasar was more red or blue, a measurement that then automatically adjusted the angle of a polarizer that ultimately received and detected the incoming entangled photon.

“The timing is very tricky,” Kaiser says. “Everything has to happen within very tight windows, updating every microsecond or so.”

Demystifying a mirage

The researchers ran their experiment twice, each for around 15 minutes and with two different pairs of quasars. For each run, they measured 17,663 and 12,420 pairs of entangled photons, respectively. Within hours of closing the telescope domes and looking through preliminary data, the team could tell there were strong correlations among the photon pairs, beyond the limit that Bell calculated, indicating that the photons were correlated in a quantum-mechanical manner.

Guth led a more detailed analysis to calculate the chance, however slight, that a classical mechanism might have produced the correlations the team observed.

He calculated that, for the best of the two runs, the probability that a mechanism based on classical physics could have achieved the observed correlation was about 10 to the minus 20 — that is, about one part in one hundred billion billion, “outrageously small,” Guth says. For comparison, researchers have estimated the probability that the discovery of the Higgs boson was just a chance fluke to be about one in a billion.

“We certainly made it unbelievably implausible that a local realistic theory could be underlying the physics of the universe,” Guth says.

And yet, there is still a small opening for the freedom-of-choice loophole. To limit it even further, the team is entertaining ideas of looking even further back in time, to use sources such as cosmic microwave background photons that were emitted as leftover radiation immediately following the Big Bang, though such experiments would present a host of new technical challenges.

“It is fun to think about new types of experiments we can design in the future, but for now, we are very pleased that we were able to address this particular loophole so dramatically. Our experiment with quasars puts extremely tight constraints on various alternatives to quantum mechanics. As strange as quantum mechanics may seem, it continues to match every experimental test we can devise,” Kaiser says.

This research was supported in part by the Austrian Academy of Sciences, the Austrian Science Fund, the U.S. National Science Foundation, and the U.S. Department of Energy.

## Share this news article on:

Press mentions.

Gizmodo reporter Ryan Mandelbaum writes that by studying ancient quasars, MIT scientists have uncovered evidence supporting quantum entanglement, the concept that two particles can become linked despite their distance in space and time. “We’ve outsourced randomness to the furthest quarters of the universe, tens of billions of light years away,” says Prof. David Kaiser.

Space.com reporter Chelsea Gohd writes that MIT researchers have used the light emitted by two ancient quasars to provide evidence of quantum entanglement, the theory that two particles can become linked across space and time. The researchers used ancient quasars to see if, “the correlation between particles can be explained by classical mechanics stemming from earlier than 600 years ago.”

## Motherboard

Writing for Motherboard , Daniel Oberhaus highlights how MIT researchers have used light emitted by quasars billions of years ago to confirm the existence of quantum entanglement. Oberhaus explains that the findings suggest entanglement occurs “because if it didn’t exist the universe would somehow have to have ‘known’ 7.8 billion years ago that these MIT scientists would perform these experiments in 2018.”

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- Published: 19 December 2018

## Entanglement certification from theory to experiment

- Nicolai Friis ORCID: orcid.org/0000-0003-1950-8640 1 ,
- Giuseppe Vitagliano 1 ,
- Mehul Malik 1 , 2 &
- Marcus Huber ORCID: orcid.org/0000-0003-1985-4623 1

Nature Reviews Physics volume 1 , pages 72–87 ( 2019 ) Cite this article

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- Quantum information
- Quantum optics

Entanglement is an important resource for quantum technologies. There are many ways quantum systems can be entangled, ranging from the two-qubit case to entanglement in high dimensions or between many parties. Consequently, many entanglement quantifiers and classifiers exist, corresponding to different operational paradigms and mathematical techniques. However, for most quantum systems, exactly quantifying the amount of entanglement is extremely demanding, if at all possible. Furthermore, it is difficult to experimentally control and measure complex quantum states. Therefore, there are various approaches to experimentally detect and certify entanglement when exact quantification is not an option. The applicability and performance of these methods strongly depend on the assumptions regarding the involved quantum states and measurements, in short, on the available prior information about the quantum system. In this Review, we discuss the most commonly used quantifiers of entanglement and survey the state-of-the-art detection and certification methods, including their respective underlying assumptions, from both a theoretical and an experimental point of view.

Entanglement detection and certification are of high significance for ensuring the security of quantum communication, improving the sensitivity of sensing devices, and benchmarking devices for quantum computation and simulation.

Recent years have seen continuous progress in the development of tools for entanglement certification and an increase in control over a wide variety of experimental setups suitable for entanglement creation.

Goals for the development of entanglement detection techniques are device-independence and assumption-free certification.

Current challenges include the extension of well-understood methods for two qubits to many-body and/or high-dimensional quantum systems and their application in entanglement experiments with ions, atoms and photons.

An important focus of recent research is the reduction in the number of measurements required for entanglement certification to cope with increasing system dimensions.

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## Quantum networks self-test all entangled states

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## Acknowledgements

The authors acknowledge support from the Austrian Science Fund (FWF) through the START project Y879-N27 and from the joint Czech–Austrian project MultiQUEST (I3053-N27 and GF17-33780L). N.F. acknowledges support from the FWF through project P 31339-N27. M.M. acknowledges support from the QuantERA ERA-NET co-fund (FWF Project I3773-N36) and from the UK Engineering and Physical Sciences Research Council (EPSRC) (EP/P024114/1). G.V. acknowledges support from the FWF through the Lise-Meitner project M 2462-N27.

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Nicolai Friis, Giuseppe Vitagliano, Mehul Malik & Marcus Huber

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Friis, N., Vitagliano, G., Malik, M. et al. Entanglement certification from theory to experiment. Nat Rev Phys 1 , 72–87 (2019). https://doi.org/10.1038/s42254-018-0003-5

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Published : 19 December 2018

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DOI : https://doi.org/10.1038/s42254-018-0003-5

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## What Is Quantum Entanglement? A Physicist Explains Einstein’s “Spooky Action at a Distance”

Quantum entanglement is a phenomenon in which the quantum states of two or more objects become correlated, meaning that the state of one object can affect the state of the other(s) even if the objects are separated by large distances. This occurs because, according to quantum theory, particles can exist in multiple states at the same time (a concept known as superposition) and can be inextricably linked, or “entangled,” even if they are physically separated.

Three researchers were awarded the 2022 Nobel Prize in Physics for their ground-breaking work in understanding quantum entanglement, one of nature’s most puzzling phenomena.

Quantum entanglement, in the simplest terms, means that aspects of one particle of an entangled pair depend on aspects of the other particle, no matter how far apart they are or what lies between them. These particles could be, for example, electrons or photons, and an aspect could be the state it is in, such as whether it is “spinning” in one direction or another.

The strange part of quantum entanglement is that when you measure something about one particle in an entangled pair, you immediately know something about the other particle, even if they are millions of light years apart. This odd connection between the two particles is instantaneous, seemingly breaking a fundamental law of the universe . This is why Albert Einstein famously called the phenomenon “spooky action at a distance.”

Having spent the better part of two decades conducting experiments rooted in quantum mechanics , I have come to accept its strangeness. Thanks to ever more precise and reliable instruments and the work of this year’s Nobel winners, Alain Aspect, John Clauser, and Anton Zeilinger, physicists now integrate quantum phenomena into their knowledge of the world with an exceptional degree of certainty.

However, even until the 1970s, researchers were still divided over whether quantum entanglement was a real phenomenon. And for good reasons – who would dare contradict the great Einstein, who himself doubted it? It took the development of new experimental technology and bold researchers to finally put this mystery to rest.

## Existing in multiple states at once

To truly understand the spookiness of quantum entanglement, it is important to first understand quantum superposition . Quantum superposition is the idea that particles exist in multiple states at once. When a measurement is performed, it is as if the particle selects one of the states in the superposition.

For example, many particles have an attribute called spin that is measured either as “up” or “down” for a given orientation of the analyzer. But until you measure the spin of a particle, it simultaneously exists in a superposition of spin up and spin down.

There is a probability attached to each state, and it is possible to predict the average outcome from many measurements. The likelihood of a single measurement being up or down depends on these probabilities, but is itself unpredictable .

Though very weird, the mathematics and a vast number of experiments have shown that quantum mechanics correctly describes physical reality.

## Two entangled particles

The spookiness of quantum entanglement emerges from the reality of quantum superposition, and was clear to the founding fathers of quantum mechanics who developed the theory in the 1920s and 1930s.

To create entangled particles you essentially break a system into two, where the sum of the parts is known. For example, you can split a particle with spin of zero into two particles that necessarily will have opposite spins so that their sum is zero.

In 1935, Albert Einstein, Boris Podolsky, and Nathan Rosen published a paper that describes a thought experiment designed to illustrate a seeming absurdity of quantum entanglement that challenged a foundational law of the universe.

A simplified version of this thought experiment , attributed to David Bohm, considers the decay of a particle called the pi meson. When this particle decays, it produces an electron and a positron that have opposite spin and are moving away from each other. Therefore, if the electron spin is measured to be up, then the measured spin of the positron could only be down, and vice versa. This is true even if the particles are billions of miles apart.

This would be fine if the measurement of the electron spin were always up and the measured spin of the positron were always down. But because of quantum mechanics, the spin of each particle is both part up and part down until it is measured. Only when the measurement occurs does the quantum state of the spin “collapse” into either up or down – instantaneously collapsing the other particle into the opposite spin. This seems to suggest that the particles communicate with each other through some means that moves faster than the speed of light. But according to the laws of physics, nothing can travel faster than the speed of light. Surely the measured state of one particle cannot instantaneously determine the state of another particle at the far end of the universe?

Physicists, including Einstein, proposed a number of alternative interpretations of quantum entanglement in the 1930s. They theorized there was some unknown property – dubbed hidden variables – that determined the state of a particle before measurement . But at the time, physicists did not have the technology nor a definition of a clear measurement that could test whether quantum theory needed to be modified to include hidden variables.

## Disproving a theory

It took until the 1960s before there were any clues to an answer. John Bell, a brilliant Irish physicist who did not live to receive the Nobel Prize, devised a scheme to test whether the notion of hidden variables made sense.

Bell produced an equation now known as Bell’s inequality that is always correct – and only correct – for hidden variable theories, and not always for quantum mechanics. Thus, if Bell’s equation was found not to be satisfied in a real-world experiment, local hidden variable theories can be ruled out as an explanation for quantum entanglement.

The experiments of the 2022 Nobel laureates, particularly those of Alain Aspect , were the first tests of the Bell inequality . The experiments used entangled photons, rather than pairs of an electron and a positron, as in many thought experiments. The results conclusively ruled out the existence of hidden variables, a mysterious attribute that would predetermine the states of entangled particles. Collectively, these and many follow-up experiments have vindicated quantum mechanics. Objects can be correlated over large distances in ways that physics before quantum mechanics can not explain.

Importantly, there is also no conflict with special relativity, which forbids faster-than-light communication . The fact that measurements over vast distances are correlated does not imply that information is transmitted between the particles. Two parties far apart performing measurements on entangled particles cannot use the phenomenon to pass along information faster than the speed of light.

Today, physicists continue to research quantum entanglement and investigate potential practical applications . Although quantum mechanics can predict the probability of a measurement with incredible accuracy , many researchers remain skeptical that it provides a complete description of reality. One thing is certain, though. Much remains to be said about the mysterious world of quantum mechanics.

Written by Andreas Muller, Associate Professor of Physics, University of South Florida.

## Related Articles

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If we do not know how the topological vortex gravitational field is formed, we will not know what is true science. From accretion disks to quantum spins, topological vortices are ubiquitous, and their essence is equilibrium.

I wish someday I’ll find an article or something that actually explains how these experiments and observations are done. Is everything based solely on mathematical formulas, because the conclusion that entanglement remains active millions of miles away must be. The article talks about this thought experiment lead to that thought experiment. Is all this based on thought experiments and equations, or are there real world, no kidding, observations of this stuff happening?

It’s real. And there Are many articles about it. I was zoo lazy to read this articles because it uses Einstein as a clickbait, but look for instance the double slot experiment, wave/particle duality or complementarity

Hi that’s exactly what I was won3

No, it isn’t “both up and down.” It’s that you don’t know. You never measure the particle as having up and down spin at the same time. You mathematically see a probability for each possibility.

I don’t have a good metaphor for this, bit to me it’s like saying that until a coin settles on the table (ie the future point where you “measure” it) there is a 50% probability that it’s heads and the same that it’s tails.

How in the world 🌎 do they know particles are entangled when separate across light years? A thought is not an experiment!

The previous comments illustrate how unsatisfying the article was. Here’s a different way to explain QE.

The two ways physicists have used to answer Quantum Entanglement are that the particles contain hidden variables of unknown natures or that the universe is completely deterministic with all results predefined. Both have been shown to be incorrect.

Perhaps concepts in String Theory can help. There are 11 possible dimensions in String Theory and I suggest one of them leads a way around, what Einstein called this “spooky action at a distance”. Specifics on this can be found by searching YouTube for “Quantum Entanglement – A String Theory Way”

I’m still having trouble wrapping my mind around particles syncing their moves with their dance partners without communication over great distances. Perhaps they are connected ‘interdimensionality’. Basically a hidden shortcut.

Oh, how I wish I could understand what the hell you are talking about.

So photons can’t inflow in vaccum space they needs atomic environment & molecules to move

So photons can’t influence through the vacuum space they needs atomic environment & molecules to move

So , in theory , if we cloned a person and put them on another life supporting planet , does that mean that basically we can predict the futer as to how that person will behave , simply by observing the ” earthbound ” twin clone? ( regardless of environmental influence or factors ). Or are they talking about space / time travel based on literally sending physical matter to another location based on the fact that it can fit perfectly into another matter’s location or position?

Im one of the sub-particles in the quatum entanglement experiments.. I feel their cell phone ring,when they get hurt.. the others were killed alot of them too,since the beginning of 2021 a lot of messed up things have happened best tjing ti happen is I learned I’m not a schizophrenic. But I would like to meet some of you all,my coordinates are 30.650752 by 81.5280?? Close enough I hear the plane and helicopters.. best part is you have opened a door in my mind to where my subconscious leaves and goes to extraterrestrial planets or dimensions very scary places.. I can also control robotics and people some times.. I think whatever is happening is highly secretive and classified as top secret so under discretion of secrecy please COME TO ME I’ve never met any of you but why am I able to hear you,Kno wht you ate for breakfast,you know who I am,I am the rayonier kid,and quit listening to those fake ass wanbbes with the chips in their head listening to my magic frequency,it’s all from me,put me THOMAS great great grandson of St Thomas the Pope and Mother Mary..don’t believe the imposter thts why none of your work adds up or is always incorrect,I can give you correct results any place any time or any day if the f**king week,im 33 years old,Smoke is a code name and so is He’s in Orange for agent orange,di you want to know the unknown or unlock the secrets to the cosmos,then do it and come to me,don’t say you want to if you’re not going to. I’m the voice on tht radio,I can tell you things tht they’ll never be able to or show you things,I out a F**king candle out with my mind.. but this sh*t won’t ever make it to you, NSA or HLS CIA will catch it before it is ever made Public. Hi guys n Ms “Rhonda” I’m ready to come home now. Those things are getting closer and closer to us,I’m scared now,sry about moving those way up there I’ll quit if you come take me to Langley,I getting home sick,what is wrong with me,why do u remember so much but can’t say it how come I hear somebody 24.7 and who are they the scary ones not the nice one,and why did he put a bed there many years ago?

What we call matter, particle is quantum entanglement. Matter turn into light and light into matter endlessly; at the subatomic and at the universe, like a fractal.

Is existence real? Is the demon of Descartes playing with space time? Is mc Taggart right: is time not real? If the eternal origin is void (sunyata)(zero point energy) then quantum entanglement is a monad (holon) primordial to space time

How do you know that two particles are entangled? Are you consciously creating that which is your expectation? Math is reductive, it excludes differentials and all nuance ; it is not the language of the cosmos, of infinite possibility.

Issue is not whether particles remain correlated even if they travel light years apart the issue No one seems to want to address is if one particle interact with external fields and forces while other does not then what happens to correlation? If the one which did not experience external forces changes its state to remain correlated then experimentally I can show that it is not true. For example in Mach zhender interferometer two photons traveling two seperate paths go through seperate phase change to produce interference if what happens to one happens to the other one because they are entangled then one can no ever have the interference due to phase change in one path.

Is consciousness faster than the speed of light? If so perhaps space and time lose their meaning. Therefore perhaps communication is instantaneous. That’s If you believe everything has consciousness.

For me I think that quantum entanglement is real. Right now we may not have all it takes to explain it in a simple lay man term but someday we will. But it is well established that objects tends to exist in different states and at multiple places until they are sought after. It all boils to space and time. We know that time is relative and passes differently for each observer. It can move faster or slower depending on the conveying medium or the universal dimension the object is placed in. And the ever expanding universe is intricately linked with time. Objects move in this stream of space time. Thus entangled objects each placed at the far end of the universe is still within the concept of space and time. This linking relationship makes it possible for the state of one entangled object to be altered by measuring either of them at millions of light years away from each other. We can convinently say that this kind measurement or’communication’ takes place beyond the speed of light. To try to wrap our head around it we ask ‘ what was there before the speed of light?’ Well you can’t rule out space and time. These two form the basis for the speed of light. Now what happens when we multiply these two quantities instead of dividing them? Then we get something faster than the speed of light.

Bosons can share the same position in space, thus a superposition of CW and CCW circular polarization states can exist seemingly in the same particle of light. Fermions (matter) with a similar capacity seem to be as unrealistic as Schrodinger’s half-here/half-there cats.

Some people say buckyballs show interference and thus they show a wave-like nature, I suppose buckyballs show a spin-like nature and thus only interfere with another’s detectability by having opposing net quantum spins.

The nonsense càn not explain nonsense!!??

QE particle properties having remote synchronicity is yet another of the truly exemplary demonstrations of our universe that our own human, mortal understanding of ourselves and the world around us will always shortfall the mark of truth so long as we continue in our refusal to acknowledge the mystical and metaphysical, even supernatural and spiritual aspects of reality as being intrinsically linked in with even the most rigidly physical and material laws of nature. To me, it is a beautiful thing when even bleeding edge science must admit there is more to the picture than what it can visibly render in any clear and concise way without leaving room to consider that perhaps not every attribute tying our world together can be proven to be purely physical and existential but rather that some thing might well end out being every but as much an abstraction as it was at the very first. Maybe particles are synchronized as much by God’s laws as they are by their own internal dynamics?

Here is classical non quantum entanglement. I have two billiard balls red and white. I put them into two black bags which are indistinguishable from each other. I mix them.up so do not know in which bag a given ball is. I send one bag in a rocket to the planet Neptune. What is the colour of the ball on Neptune? I do not know, but if I open the bag left on earth, I instantly know the colour of the ball on Neptune. That information has travelled much faster than light

Guys 😂, what’s going in quantum entanglement is non-dualism, the particles are not separate but one( interconnected by an infinite dimension called “pure consciousness” ), just like the yin and yang symbol, what science is trying to convey is the exact same thing that Spirituality had been trying to tell humanity for thousands of years that what’s going on this this space and time reality is ultimately an illusion and is mainly governed by an” invisible reality” called non-duality( a reality that exist beyond time, space, forms , concepts ect.. which you cannot see, touch, smell, feel or understand.). Those particles were never separated in the first place and has always been and will always be one. This physical universe that operates as space and time is an illusion,but there is another Reality(dimension ) which is the source of all the things happening in this universe. Every form,space,time language, concepts, relatively and understanding all ceases to exist and what’s left is pure energy, the consciousness itself beyond duality. Science and spirituality are so very close to be best friends,this is because science is now catching up with Spirituality has figured this whole thing out ,for a very long time ago, provlaby for more than 10 000 years.If you Go to any spiritual teacher or any yogi master ,they are going to explain this whole thing of quantum entanglement to you simply and it will make your head spin. What is going in quantum entanglement seems like magic to some people, but it’s not, it’s just science that we haven’t figure out yet. What’s happening in quantum entanglement is technology. As I have said before there is an “invisible reality” operating behind the scenes that connects this particles and it is source of all things happening in this universe of relativity.

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Physicists Maxwell Block (left) and Bingtian Ye describe how they’ve put spin squeezing within better reach.

Courtesy of Yao Lab

## Spin squeezing for all

Physicists ease path to entanglement for quantum sensing

Anne J. Manning

Harvard Staff Writer

Nothing in science can be achieved or understood without measurement. Today, thanks to advances in quantum sensing, scientists can measure things that were once impossible to even imagine: vibrations of atoms, properties of individual photons, fluctuations associated with gravitational waves.

A quantum mechanical trick called “spin squeezing” is widely recognized to hold promise for supercharging the capabilities of the world’s most precise quantum sensors, but it’s been notoriously difficult to achieve. In new research, Harvard physicists describe how they’ve put spin squeezing within closer reach.

A type of quantum entanglement, spin squeezing constrains the way an ensemble of particles can fluctuate. This enables more precise measurements of certain observable signals, at the expense of measuring other, complementary signals as accurately — think of how squeezing a balloon yields more height at the expense of width.

“Quantum mechanics can enhance our ability to measure very small signals,” said Norman Yao , a physics professor and author of the new paper on spin squeezing in Nature Physics . “We have shown that it is possible to get such quantum-enhanced metrology in a much broader class of systems than was previously thought.”

In the balloon metaphor, a circle represents the uncertainty intrinsic to any quantum measurement, explained Maxwell Block, co-author of the paper and a former Griffin Graduate School of Arts and Sciences student. “By squeezing this uncertainty, making the balloon more like an ellipse, one can reshape the sensitivity of measurements,” Block said. “This means that certain measurements can be more precise than anything one could possibly do without quantum mechanics.”

Spin squeezing is a form of quantum entanglement that can enable more precise measurements (middle). Previously known to arise only in all-to-all interacting systems (left), Harvard researchers have shown that spin squeezing can occur more generally in locally interacting systems that form planar magnets (right).

Credit: Bingtian Ye

An analog of spin squeezing was used, for example, to increase the sensitivity of the Nobel-garnering gravitational wave detectors in the LIGO experiment.

The Harvard team’s work built upon a landmark 1993 paper that first described the possibility of a spin-squeezed, entangled state brought about by “all-to-all” interactions between atoms. Such interactions are akin to a large Zoom meeting, in which each participant is interacting with every other participant at once. Between atoms, this type of connectivity easily enables the build-up of the quantum mechanical correlations necessary to induce a spin-squeezed state. However, in nature, atoms typically interact in a way that’s more like a game of telephone, only speaking with a few neighbors at a time.

“For years, it has been thought that one can only get truly quantum-enhanced spin squeezing via all-to-all interactions,” said Bingtian Ye, co-lead author of the paper and also a former Griffin Graduate School of Arts and Sciences student. “But what we have shown is that it is actually way easier.”

In their paper, the researchers outline a new strategy for generating spin-squeezed entanglement. They intuited, and together with collaborators in France quickly confirmed via experiment that the ingredients for spin squeezing are present in a ubiquitous type of magnetism found often in nature — ferromagnetism, which is also the force that makes refrigerator magnets stick. They posit that all-to-all interactions are not necessary to achieve spin squeezing, but rather, so long as the spins are connected well enough to sync into a magnetic state, they should also be able to dynamically generate spin squeezing.

The researchers are optimistic that by thus lowering the barrier to spin squeezing, their work will inspire new ways for quantum scientists and engineers to create more portable sensors, useful in biomedical imaging, atomic clocks, and more.

In that spirit, Yao is now leading experiments to generate spin-squeezing in quantum sensors made out of nitrogen-vacancy centers, which are a type of defect in the crystal structure of diamond that have long been recognized as ideal quantum sensors .

The research received federal support from: the Army Research Office, the Office of Naval Research, the Department of Energy, the Department of Defense, and the National Science Foundation.

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## Physicists ease path to entanglement for quantum sensing

by Anne J. Manning, Harvard Gazette

Nothing in science can be achieved or understood without measurement. Today, thanks to advances in quantum sensing, scientists can measure things that were once impossible to even imagine: vibrations of atoms, properties of individual photons, fluctuations associated with gravitational waves.

A quantum mechanical trick called "spin squeezing" is widely recognized to hold promise for supercharging the capabilities of the world's most precise quantum sensors, but it's been notoriously difficult to achieve. In new research, Harvard physicists describe how they've put spin squeezing within better reach.

A type of quantum entanglement, spin squeezing, constrains the way an ensemble of particles can fluctuate. This enables more precise measurements of certain observable signals, at the expense of measuring other, complementary signals as accurately—think of how squeezing a balloon yields more height at the expense of width.

"Quantum mechanics can enhance our ability to measure very small signals," said Norman Yao, a physics professor and author of the paper on spin squeezing in Nature Physics . "We have shown that it is possible to get such quantum-enhanced metrology in a much broader class of systems than was previously thought."

In the balloon metaphor, a circle represents the uncertainty intrinsic to any quantum measurement, explained Maxwell Block, co-author of the paper and a former Griffin Graduate School of Arts and Sciences student.

"By squeezing this uncertainty, making the balloon more like an ellipse, one can reshape the sensitivity of measurements," Block said. "This means that certain measurements can be more precise than anything one could possibly do without quantum mechanics."

An analog of spin squeezing was used, for example, to increase the sensitivity of the Nobel-garnering gravitational wave detectors in the LIGO experiment.

The Harvard team's work built upon a landmark 1993 paper that first described the possibility of a spin-squeezed, entangled state brought about by "all-to-all" interactions between atoms. Such interactions are akin to a large Zoom meeting, in which each participant is interacting with every other participant at once.

Between atoms, this type of connectivity easily enables the build-up of the quantum mechanical correlations necessary to induce a spin-squeezed state. However, in nature, atoms typically interact in a way that's more like a game of telephone, only speaking with a few neighbors at a time.

"For years, it has been thought that one can only get truly quantum-enhanced spin squeezing via all-to-all interactions," said Bingtian Ye, co-lead author of the paper and also a former Griffin Graduate School of Arts and Sciences student. "But what we have shown is that it is actually way easier."

In their paper, the researchers outline a new strategy for generating spin-squeezed entanglement. They intuited, and together with collaborators in France quickly confirmed via experiment that the ingredients for spin squeezing are present in a ubiquitous type of magnetism found often in nature—ferromagnetism, which is also the force that makes refrigerator magnets stick.

They posit that all-to-all interactions are not necessary to achieve spin squeezing, but rather, so long as the spins are connected well enough to sync into a magnetic state, they should also be able to dynamically generate spin squeezing.

The researchers are optimistic that by thus lowering the barrier to spin squeezing, their work will inspire new ways for quantum scientists and engineers to create more portable sensors, useful in biomedical imaging, atomic clocks, and more.

In that spirit, Yao is now leading experiments to generate spin -squeezing in quantum sensors made out of nitrogen-vacancy centers, which are a type of defect in the crystal structure of diamond that have long been recognized as ideal quantum sensors.

Journal information: Nature Physics

Provided by Harvard Gazette

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## Quantum Entanglement

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Quantum entanglement occurs when a system of multiple particles in quantum mechanics interact in such a way so that the particles cannot be described as independent systems but only as one system as a whole. Measurement (e.g. of the spin of an entangled electron) may instantaneously affect another electron's spin at an arbitrarily distant location, apparently (but not actually) faster than the lightspeed limit of special relativity . The fact that electron spin measurements can be highly correlated, violating Bell's inequality , is one of the cornerstone experimental results in the modern theory and interpretation of quantum mechanics.

The properties of quantum entanglement may engender quantum teleportation , where the state of one entangled particle is sent from one location to another without moving the particle. This phenomenon may prove extremely useful in the nascent field of quantum computing , where manipulating quantum states without losing information by exposing them to the environment is highly valued.

In quantum entanglement, measurements of the spin state of one particle influence the spin state of another arbitrarily distant particle with which the first is entangled.

## EPR Paradox and Stern-Gerlach Experiments

Measurement of electron spin, entanglement and tensor products.

The original Stern-Gerlach experiment examined the behavior of silver atoms in magnetic fields . Magnetic dipoles couple to magnetic fields; they feel a force \(F = \nabla (\vec{\mu} \cdot \vec{B})\) where \(\mu\) is the magnetic dipole moment and \(B\) is the magnetic field vector. Since silver atoms only have one valence electron with zero orbital angular momentum (a \(5s\) electron), any coupling of silver atoms to magnetic fields is due to an intrinsic magnetic dipole moment or spin of the electron. Since only the behavior of the valence electron matters, the rest of this article will refer to electrons where silver atoms were actually used originally.

In the Stern-Gerlach experiment, the magnetic field gradient \(\nabla B\) is aligned along the z-axis and set to some constant \(C\) so that electrons are deflected in the magnetic field according to the magnetic dipole moment: \(F = C\mu\). If the electrons are spin-up in the z-direction, they are deflected upwards, whereas if the electrons are spin-down in the z-direction, they are deflected downwards. This experiment provided the first evidence for the quantization of spin: on a detecting screen behind the magnets, only two peaks appear rather than a continuous spectrum, corresponding to the two possible quantized values of spin rather than a continuous distribution of possible magnetic dipole moments.

Experimental setup of a Stern-Gerlach experiment. An electron source beams electrons into a magnetic gradient, where they are deflected according to their intrinsic magnetic moment. Only two peaks are detected beyond the magnets, corresponding to the two possible spin values.

The entirety of a Stern-Gerlach experiment can be thought of as a black box which is able to measure whether an entering electron is spin-up or spin down.

In the EPR thought experiment, Einstein, Podolsky, and Rosen considered a system of two electrons which are sent in opposite directions through two Stern-Gerlach apparatuses, measuring each of their spins. If the electrons are entangled , then when electron 1 is measured to be spin-up, electron 2 is measured to be spin-down a large percentage of the time, and vice versa. The precise meaning of "entangled" in quantum mechanics is discussed below mathematically. The result seemed to imply that at one Stern-Gerlach apparatus, the measurement result was being communicated instantly to the other apparatus. Although EPR did not perform the experiment themselves, actual experimental results are consistent with their mathematics. The nonlocality of the EPR paradox would be in violation of the principles of relativity, since it seems like information is being communicated to a distant location faster than the speed of light.

Setup of EPR's thought experiments: spin-entangled electrons are sent in opposite directions to two distant Stern-Gerlach apparatuses, where their spins are measured, revealing remarkable correlations.

EPR tried to avoid this conclusion by asserting that there must have been some local hidden variables : at the electron source, some variable that cannot be measured was determining the outcomes of spin measurements when the entangled electrons were produced. They took this to mean that the theory of quantum mechanics was not complete, since the spin and spatial wavefunctions of the electrons did not include the hidden variables and so could not account for all the physics that they would observe. However, in the 1960s, Bell's theorem showed that this was not the case: no local hidden variables theory could possibly account for the degree of correlation present in measurement of spin-entangled electrons.

Entanglement usually originates on the subatomic scale via processes that produce two electrons simultaneously in a correlated way, although complicated systems of fiber optics can be used to produce e.g. systems of two photons with entangled polarizations.

A single electron spin in quantum mechanics is described by a vector in a two-dimensional vector space . The basis vectors are taken to be the eigenvectors of the \(\hat{S}_z\) operator giving the spin of the electron along the \(z\) axis, and are labeled \(|0\rangle\) and \(|1\rangle\), \(|+\rangle\) and \(|-\rangle\), or \(|\uparrow\rangle\) and \(|\downarrow\rangle\) depending on context. In this article, the latter notation will be used. In general, an arbitrary electron spin state can be a superposition of the "spin-up" and "spin-down" states:

\[|\Psi\rangle = c_1 |\uparrow\rangle + c_2 |\downarrow\rangle,\]

where \(c_1\) and \(c_2\) are some complex constants normalized so that \(|c_1|^2+|c_2|^2 = 1\). This notation suggests that a single-spin state can be written as a vector:

\[|\Psi \rangle = \begin{pmatrix} c_1 \\ c_2 \end{pmatrix}.\]

The spin states are defined so that the spin operator in the z-direction,

\[\hat{S}_z = \frac{\hbar}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix},\]

has eigenvalues \(\pm\frac{\hbar}{2}\) corresponding to the eigenvectors \(|\uparrow\rangle\) and \(|\downarrow\rangle\). This operator acts on the vector representation of spin states by simple matrix multiplication.

A electron spin in quantum mechanics is given by the superposition state:

\[\large |\Psi\rangle = \frac{i}{2} |\uparrow\rangle + \dfrac{\sqrt{3}}{2} |\downarrow\rangle.\]

What is the probability of measuring the spin in the \(z\)-direction to have value equal to \(-\dfrac{\hbar}{2}\)?

In a two-particle system, the spins of two electrons can be described jointly using tensor product spaces . The tensor product of two electron spin states lives in a four-dimensional vector space, with basis vectors labeled:

\[|\uparrow\rangle\otimes|\uparrow\rangle, \quad |\uparrow\rangle\otimes|\downarrow\rangle, \quad |\downarrow\rangle\otimes|\uparrow\rangle, \quad |\downarrow\rangle\otimes|\downarrow\rangle.\]

The tensor product of two states \(|x\rangle\) and \(|y\rangle\) obeys the following rules:

1) Scaling the tensor product is equivalent to scaling either state:

\[c(|x\rangle \otimes |y\rangle) = (c|x\rangle) \otimes |y\rangle = |x\rangle \otimes (c|y\rangle).\]

2) The tensor product is distributive in both the first and second slots:

\[ \begin{align} &|x\rangle \otimes (|y_1\rangle + |y_2\rangle) = |x\rangle \otimes |y_1\rangle + |x\rangle\otimes |y_2\rangle \\ &(|x_1\rangle + |x_2\rangle) \otimes |y\rangle = |x_1\rangle \otimes |y\rangle + |x_2\rangle\otimes |y\rangle \end{align} \]

An arbitrary tensor product state for a two-spin system can be written out in the four-dimensional basis as:

\[|\Psi\rangle = c_{11} |\uparrow\rangle\otimes|\uparrow\rangle + c_{12} |\uparrow\rangle\otimes|\downarrow\rangle + c_{21} |\downarrow\rangle\otimes|\uparrow\rangle + c_{22} |\downarrow\rangle\otimes|\downarrow\rangle.\]

Two spin state are given by \(|\Psi_1\rangle = |\uparrow\rangle\) and \(|\Psi_2 \rangle = \frac{1}{\sqrt{2}} (|\uparrow\rangle + |\downarrow\rangle)\).

Which gives the correct tensor product state \(|\Psi_1 \rangle \otimes |\Psi_2\rangle\)?

Note : The notation \(|\uparrow\downarrow\rangle = |\uparrow\rangle \otimes |\downarrow\rangle\) is a common shorthand for tensor products of spin states.

This notation suggests that it is more convenient to represent a two-spin state as a matrix, in analogue to the vector representation of a one-spin state:

\[|\Psi \rangle = \begin{pmatrix} c_{11} & c_{12} \\ c_{21} & c_{22} \end{pmatrix}.\]

To perform a measurement on a two-spin system, one needs to specify the operators acting on each independent space. For instance, to measure the spin of just the first particle, use the operator written as \(\hat{S}_z \otimes I\), which measures the spin of the first particle in the z-direction and acts on the second space as the identity. To measure the spins in the z-direction of both particles simultaneously, use \(\hat{S}_z \otimes \hat{S}_z\) and so on.

Having defined this notation, it is now possible to state an explicit mathematical criterion of entanglement that is useful for proving things in quantum information theory.

A two-electron spin state is a product state if it can be written as the tensor product of exactly two independent single-spin states.

Some states are obviously product states: \(|\uparrow\rangle \otimes |\downarrow\rangle\), for instance, is clearly the product of \(|\uparrow\rangle\) and \(|\downarrow\rangle\). This state, therefore, can be described just by taking each independent single-spin state independently and ignoring the other. A state such as \(|\uparrow\rangle \otimes |\downarrow\rangle + |\downarrow\rangle \otimes |\uparrow\rangle\), however, is clearly not a product state. Not all cases are so obvious, however, which is why formulating a precise mathematical criterion is important.

The intuition above suggests the definition of entanglement:

A two-electron spin state is entangled if it is not a product state, that is, if the matrix representation \(M\) of the state does not satisfy \(\det M = 0\).

For states of more than two electrons, this condition is actually too strong -- if \(\det M \neq 0\), then all of the electron spins are entangled. But it's enough for just two of the electrons to be entangled in a multiparticle state for the whole state to be considered entangled. The more accurate condition for a general multiparticle state is that \(\text{rank } M \geq 2\), since this is equivalent to entanglement in a two-dimensional subspace. Note that this condition reduces to \(\det M \neq 0\) for a two-electron spin state.

Challenge problem: prove the determinant condition for entanglement described above

Is the following state \(|\Psi\rangle\) entangled?

\[|\Psi\rangle = \frac{1}{\sqrt{2}} (|\downarrow\downarrow\rangle + |\downarrow\uparrow\rangle).\]

\[|\Psi\rangle = \frac{1}{\sqrt{5}}|\uparrow\uparrow\rangle +\frac{\sqrt{2}}{\sqrt{5}} |\downarrow\uparrow\rangle - \frac{\sqrt{2}}{\sqrt{5}} |\downarrow\downarrow\rangle\]

Is the state \(|\Psi\rangle\) above entangled?

The reason for this definition of entanglement is as described above. If a two-spin state can be written as a product state, it is as if each spin is independent. Measurements on each spin do not affect the other. But if a two-spin state is entangled, the fact that the the state is not a product state means that collapsing to one eigenvector in one space causes collapse in the other space as well. Measurements on one spin thus affect any entangled spins instantaneously by influencing what measurements of the other spin are possible, regardless of the spatial location of the other electron! It is important to note, however, that this is not in violation of special relativity: information cannot be sent faster than lightspeed via entanglement; the effects of entanglement can only be seen after the fact when two observers meet up to compare spin measurements.

Consider the entangled state given by: \[|\Psi_E \rangle =\frac{1}{\sqrt{2}} ( |\uparrow\rangle \otimes |\downarrow\rangle - |\downarrow\rangle \otimes |\uparrow\rangle),\] and the non-entangled state given by \[|\Psi_N \rangle = \frac{1}{\sqrt{2}}( |\uparrow\rangle \otimes |\uparrow\rangle + |\uparrow\rangle \otimes |\downarrow\rangle).\] Show that measuring the spin of the first particle for \(|\Psi_E\rangle\) affects the probabilities of finding the second particle in each possible state, while the same measurement for \(|\Psi_N\rangle\) does not affect the results. Solution: For the entangled state, before measurement the second particle has an equal chance to be found in either the spin-up or spin-down states. After measurement of the first particle's spin with the operator \(\hat{S}_z \otimes I\), if the first electron is found in the spin-up state, \(|\Psi_E\rangle\) collapses to \(|\uparrow \rangle \otimes |\downarrow\rangle\) and the second electron must be found in the spin-down state. If the first electron is found in the spin-down state the reverse is true; thus, measurement of the state of the first electron has affected the overall state of the system. For the non-entangled state, the probability of finding the first particle in the spin-up state is one. After measurement, the state does not change, and the second particle is still in an equal superposition of both spin states. Note that there also exist non-entangled states for which measuring the first particle would change the overall spin wavefunction without changing the state of the second particle.

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August 20, 2024

12 min read

## Can Space and Time Exist as Two Shapes at Once? Mind-Bending Experiments Aim to Find Out

Proposed experiments will search for signs that spacetime is quantum and can exist in a superposition of multiple shapes at once

By Nick Huggett & Carlo Rovelli

T here is a glaring gap in our knowledge of the physical world: none of our well-established theories describe gravity’s quantum nature. Yet physicists expect that this quantum nature is essential for explaining extreme situations such as the very early universe and the deep interior of black holes. The need to understand it is called the problem of “ quantum gravity .”

The established classical concept of gravity is Einstein’s general theory of relativity. This spectacularly successful theory has correctly predicted phenomena from the bending of light and the orbit of Mercury to black holes and gravitational waves. It teaches us that the geometry of space and time—spacetime—is determined by gravity. So when we talk about the quantum behavior of gravity, we’re really talking about the quantum behavior of spacetime.

We don’t currently have an established theory of quantum gravity, but we do have some tentative theories. Among them, loop quantum gravity (which one of us, Rovelli, helped to develop) and string theory are two leading contenders. The former predicts that the fabric of spacetime is woven from a network of tiny loops, whereas the latter posits that particles are fundamentally vibrating strings.

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Testing these theories is difficult because we can’t study the early universe or black hole interiors in a laboratory. Physicists have mostly assumed that experiments that could directly tell us something about quantum gravity require technology that is many years away.

This situation might be changing. Recent developments suggest it may be possible to perform laboratory experiments that will reveal something about the quantum behavior of gravity. This potential is extremely exciting, and it has raised real enthusiasm among theoretical and experimental physicists, who are actively trying to develop the means to carry out the investigations. The proposed experiments could test the predictions of quantum gravity theories and provide support for the assumptions they’re based on.

The experiments all involve events happening at low energies, where the predictions of strings, loops, and the like agree, so they aren’t going to tell us which specific theory of quantum gravity is correct. Still, experimental evidence that gravity is actually quantized would be groundbreaking.

We already have plenty of observations about gravity’s effects on the quantum behavior of matter. Albert Einstein’s theory works fine in these situations, from stellar dynamics, to the cosmological formation of galaxy clusters, all the way to laboratory experiments on the effect of Earth’s gravity on quantum systems. But in all these scenarios, gravity itself behaves in a way that is consistent with classical physics; its quantum features are irrelevant. What’s much more difficult is to observe phenomena in which we expect gravity to behave quantum mechanically.

We both have worked on quantum gravity throughout our careers—Rovelli as a physicist and Huggett as a philosopher. We are keenly interested in exploring what these experiments can and cannot tell us about quantum gravity. If they come to fruition, we might be able to see, for the first time, space and time themselves being quantum.

T he two of us were discussing the developments recently during a break at a conference. Over coffee in a café in Oxford, England, we came up with a simple thought experiment illustrating how the quantum nature of gravity could be revealed. (Related ideas have been discussed previously by, for instance, Alejandro Perez of Aix-Marseille University in France, in work on dark-matter detection, and Netanel H. Lindner and Asher Peres of the Technion–Israel Institute of Technology.)

Our idea involves “interference,” which has been crucial in unraveling many aspects of quantum mechanics. Interference is a phenomenon that applies to waves, quantum or not. All waves have a pattern of crests and troughs; the distance between two crests or troughs is the wavelength. If the crests of two waves meet at a point, they combine to produce a crest twice as high as either alone, and when two troughs meet, you get a trough twice as deep. This kind of interference is said to be constructive. Destructive interference, then, is when a wave and a trough overlap and cancel each other out.

Jen Christiansen

In the 19th century, interference allowed scientist Thomas Young to demonstrate that light acts like a wave. He shined light through two narrow slits to cast an image on a screen behind them. Waves from each slit travel the same distance to reach the point directly between the two slits, so their peaks hit that point at the same time, and they produce constructive interference—that’s where Young saw the brightest light. At points farther along the wall to the right of the light source, the wave from the left slit has to travel a slightly longer distance than the wave from the right, so crests and troughs no longer line up, and the height of the added waves decreases. Eventually there is a point at which the wave from the left has to travel half a wavelength farther than the one from the right, and crests line up with troughs to make destructive interference; here Young saw no light. This pattern, known as “Young’s fringes,” repeated along the wall and showed that light is, in fact, a wave.

Young’s experiment was purely classical, but variations on this setup became important for quantum physics. In 1923 physicist Louis de Broglie proposed that quantum objects may behave not like little billiard balls, as they had often been thought of, but like waves. If so, particles such as neutrons should also produce a pattern of fringes in a double-slit experiment—and indeed they do, as demonstrated in the 1980s with neutrons produced in a nuclear reactor.

Amazingly, these experiments produce the same results when neutrons pass one at a time through the double slits. Even a single neutron sent through the experiment will create interference, meaning it somehow interferes with itself . That can happen only if the neutron acts like two waves that follow two different paths. Because the idea of being in two places at once is so alien to classical particles, a new term was adopted; we say the neutron is in a “superposition” of being both here and there.

Does this part of quantum weirdness apply to gravity? Does it apply to space and time? To address these questions, we turn to general relativity, which tells us the presence of mass (or energy more generally) means that nearby spacetime will be curved. This curvature, in turn, means that objects will be naturally deflected toward mass, explaining its gravitational attraction. Such spacetime curvature also means that clocks run slower when they are closer to a mass. This effect can be used in an interference experiment that brings quantum mechanics and gravity together— a step toward showing gravity is quantum.

Suppose a neutron, in wave form, is split in two by a mirror that reflects and transmits equal amounts of the wave. The two resulting quantum waves travel different paths to a screen: one travels parallel to the ground and then upward, the other upward and thenparallel to the ground, each path forming two sides of a rectangle. The waves are in sync when they leave the mirror, but because of Earth’s gravity, the wave that follows the lower path will oscillate more slowly, and its crests will arrive slightly after those of the wave that follows the higher path. (The effect of the vertical segment is the same on both.) The result is quantum interference caused purely by the curvature of spacetime.

Physicists proposed such an experiment in 1974. The following year Roberto Colella and Albert W. Overhauser, both at Purdue University, collaborated with Samuel A. Werner, then a staff scientist at Ford Motor Company, and successfully carried it out . The team observed the predicted fringe pattern, directly demonstrating the influence of gravity on the quantum behavior of particles, to the great excitement of many scientists. But even though the neutrons in the experiment behaved quantum mechanically, gravity in this case can be described by general relativity, so it is still classical, not quantum.

The breakthrough in the new proposals is that they aim to go further and demonstrate for the first time that gravity, like neutrons and light and all other quantum objects, also has a quantum nature.

A ccording to general relativity, all matter, whether a planet, a speck of dust or a neutron, affects spacetime curvature. The deformation of spacetime produced by a small object is minuscule, but it still happens. But what if a small object is in a quantum superposition of locations? Because each position produces a different spacetime geometry, physicists expect that the result is a quantum superposition of geometries. It is as if spacetime has two shapes at once. It is this quantum weirdness of gravity that we hope to one day see in a laboratory.

The simple thought experiment we came up with that day in Oxford shows how it could be done in principle. Imagine that you shine a light past an object in superposition. That light would travel through a superposition of two spacetime geometries. In one geometry it might be far from the object, in which case the effect of gravity would be negligible, and it would travel in a straight line to a screen. In the other geometry it would pass close enough to the object that gravity would have to be taken into account, so it would follow a curved path to the screen. These two different paths mean that when the waves recombine at the screen, they will interfere and produce the telltale fringe pattern.

Crucially, interference will not arise unless gravity can exist in superposition—in other words, unless gravity itself is quantum. If instead gravity is fundamentally classical, no such interference will result. Perhaps, as mathematician and Nobel laureate Roger Penrose has argued, nature picks one of the superposed geometries, causing the mass in superposition to “choose” a single location. Or perhaps there is a single geometry corresponding to a single mass at the average position among its possible locations. Either way, there will be no superposition of geometries, and the light ray will follow a single path and won’t be able to interfere with itself. So if interference fringes were to occur in such an experiment, they would, according to standard physics, show quantumlike behavior of gravity such as a superposition of geometries—a momentous result so far not achieved by any experiment.

What are the prospects of carrying out such an experiment? On one hand, the more massive the object we place in superposition, the greater the effect on gravity and hence on the light. On the other, although every object is fundamentally quantum mechanical, most large, everyday things are essentially impossible to observe in superposition because they interact too much with their environments, hiding any interference. We call this effect “decoherence.” The larger something is, the more chances it has to interact, and the more it decoheres ; scientists who have isolated systems to overcome this effect have won Nobel Prizes.

So we are pulled in two directions for our experiment. We need something big enough to let us see gravitational effects but small enough for us to see its quantum nature. We have to find the sweet spot.

Quantum gravity is characterized by three constants of nature: the speed of light, Isaac Newton’s constant describing the strength of gravity, and Planck’s constant describing the scale of quantum phenomena. Arithmetically combining them produces a characteristic “Planck mass” of around 20 micrograms (μg). This is about the same mass as that of a flea egg or a strand of hair a few millimeters long: not large but—unlike the energy involved in the big bang—definitely on a human scale. The sweet spot where we hope to search is plausibly around this mass, which involves both gravitational and quantum mechanical constants.

Recently scientists were able to place an object of that mass into a quantum superposition of locations two billionths of a nanometer apart . This separation, however, is still less than a billionth of the distance we’d need for our tests to have a visible effect. The situation may seem hopeless, but to an experimentalist it sounds like a challenge. Labs are working hard to gain better control over the quantum behavior of Planck-mass bodies and to observe the gravitational effects of masses many times lighter than 20 μg.

If we want to observe a fringe pattern, though, we can’t just shine light at the object in superposition. Even in the gravitational field of a Planck-mass object, the effect will be too small. For us to have any chance of observing what we seek, the light would need a wavelength of 10 − 32 meter—once again in the inaccessible realm found only at the big bang.

W hat if, instead of light, we used a second quantum mass to travel near the original mass and exploited its quantum wave nature? The heavier the mass, the greater the gravitational force—and the slower it moves, the longer the mass has to experience that force. These two effects are dramatic: fringes should be observable if the two masses are one ten-thousandth of the Planck mass, tantalizingly close to current experimental ability.

In 2017 a pair of papers about another way of measuring quantum gravity effects in the lab triggered considerable excitement among physicists. The research suggests a strategy for observing a superposition of spacetime geometries that is more subtle and possibly within even closer reach than the one the two of us came up with. Both build on recent advances in theory and experiment that have brought gravity and quantum physics closer together. Both take inspiration from theoretical physicist Richard Feynman’s 1957 version of an idea originally proposed by Soviet physicist Matvei Bronstein.

Start with two Planck-mass particles, each in a quantum superposition of locations. Combined, the pair is in a superposition of four possibilities: one where they are close together, two where they are (much) farther apart and one in which they are at the greatest distance from one another in the experiment. Because the geometry of spacetime depends on the distance between the particles, the different possibilities for the particles’ arrangement correspond to different geometries. Once again, the particle superposition means that gravity, too, is in a quantum superposition.

According to quantum theory, a stationary quantum particle is a wave that oscillates with a frequency that depends on its energy, so it is a kind of clock. But as we mentioned, gravity affects the rate at which clocks run. In particular, the particles oscillate at different rates in their different arrangements: the closer they are, the slower they oscillate. As a result, the superposed arrangements get out of phase with one another. As before, when waves get out of phase, they experience interference, which in this case can be measured in characteristically quantum correlations between the two particles called “ entanglement .”

A basic result from the theory of quantum information indicates that entanglement can’t be observed unless the gravitational field through which the particles interact is in a quantum superposition. Therefore, observing the entanglement of the two particles is another means of demonstrating the quantum mechanical behavior of the gravitational field. In 2019 Rovelli published a paper with Marios Christodoulou of the Institute for Quantum Optics and Quantum Information Vienna (IQOQI) arguing that if gravity were indeed caused by deformations of the spacetime geometry, then measuring such entanglement would provide evidence that spacetime geometry can be put into superposition—that space and time, one may say, are quantum.

The 2017 proposal, and this convergence of spacetime physics with the field of quantum information, has caused a splash of experimental, theoretical and philosophical consequences. We are both members of a research consortium called Quantum Information Structure of Spacetime (QISS) that is working to elaborate theoretically and experimentally on these ideas. For instance, a group at IQOQI has been developing the experimental techniques that will be necessary for the entanglement experiment. Other groups in QISS have clarified the theoretical and philosophical significance of the experiment and proposed alternatives to measuring entanglement.

That the QISS collaboration involves philosophers such as Huggett may seem surprising. But there is a tradition of philosophical investigation of space and time that can be traced from antiquity through 17th-century polymaths Newton and Gottfried Wilhelm Leibniz, 19th-century scientist Henri Poincaré, Einstein, and many others. When foundational notions such as space and time need to be rethought, we need people who can bring in a high level of analytical and conceptual—that is, philosophical—clarity. For instance, Huggett recently explored the implications of gravitational entanglement in a book written with science philosophers Niels Linnemann and Mike D. Schneider.

T his is not the first time scientists have envisioned laboratory experiments meant to test possible quantum gravity phenomena. But all past proposals, as far as we can tell, involved either unobservably small or extremely speculative effects that aren’t actually predicted by plausible hypotheses about quantum gravity. Rovelli remembers his surprise at first encountering the idea for the new gravity-induced entanglement experiment: a phenomenon that may well become testable and that we expect to be real.

There is still a long way to go over the next few years to carry out such trials (and there would be an even longer path toward enacting our own thought experiment). But if they can be successfully accomplished, they will test the low-energy domain on which almost all theories agree. If researchers find evidence for spacetime in superposition, then they will have the first direct evidence for the basic assumptions of our theories of quantum gravity. We will substantially rule out the possibility that gravity is classical, a significant and previously unexpected step forward. More than that, experimentalists would have reached a new horizon of the physical world, producing a region of spacetime that is observably quantum in a macroscopic laboratory. At last physics will have concretely entered a realm that for now remains a land of hypothesis.

If signs of superposition are notobserved, the experiments will instead support speculations that gravity is intrinsically classical, confounding the expectations of much of the physics community and plunging a huge amount of work from the past 40 years into crisis. Such a result would require a significant revision of our understanding of the world and of the connection between quantum theory and gravity.

In either case, the effect would be momentous.

Nick Huggett is a philosopher at the University of Illinois Chicago who specializes in the philosophy of physics.

Carlo Rovelli is a theoretical physicist and writer. He is associated with Aix-Marseille University in France, the University of Western Ontario and the Perimeter Institute in Canada, and the Santa Fe Institute in New Mexico. His latest book is White Holes (Riverhead Books, 2023).

## New Classical Algorithm Enhances Understanding of Quantum Computing’s Future

In an exciting development for quantum computing, researchers from the University of Chicago’s Department of Computer Science , Pritzker School of Molecular Engineering , and Argonne National Laboratory have introduced a groundbreaking classical algorithm that simulates Gaussian boson sampling (GBS) experiments. This achievement not only helps clarify the complexities of current quantum systems but also represents a significant step forward in our understanding of how quantum and classical computing can work together. The research just appeared in the prominent Nature Physics Journal this past June.

## The Challenge of Gaussian Boson Sampling

Gaussian boson sampling has gained attention as a promising approach to demonstrating quantum advantage, meaning the ability of quantum computers to perform tasks that classical computers cannot do efficiently. The journey leading up to this breakthrough has been marked by a series of innovative experiments that tested the limits of quantum systems. Previous studies indicated that GBS is challenging for classical computers to simulate under ideal conditions. However, Assistant Professor and author Bill Fefferman pointed out that the noise and photon loss present in actual experiments create additional challenges that require careful analysis.

Notably, experiments ( such as these ) conducted by teams at major research centers from the University of Science and Technology of China and Xanadu, a Canadian quantum company, have shown that while quantum devices can produce outputs consistent with GBS predictions, the presence of noise often obscures these results, leading to questions about the claimed quantum advantage. These experiments served as a foundation for the current research, driving scientists to refine their approaches to GBS and better understand its limitations.

## Understanding Noise in Quantum Experiments

“While the theoretical groundwork has established that quantum systems can outperform classical ones, the noise present in actual experiments introduces complexities that require rigorous analysis,” explained Fefferman. “Understanding how noise affects performance is crucial as we strive for practical applications of quantum computing.”

This new algorithm addresses these complexities by leveraging the high photon loss rates common in current GBS experiments to provide a more efficient and accurate simulation. The researchers employed a classical tensor-network approach that capitalizes on the behavior of quantum states in these noisy environments, making the simulation more efficient and manageable with available computational resources.

## Breakthrough Results

Remarkably, the researchers found that their classical simulation performed better than some state-of-the-art GBS experiments in various benchmarks.

“What we’re seeing is not a failure of quantum computing, but rather an opportunity to refine our understanding of its capabilities,” Fefferman emphasized. “It allows us to improve our algorithms and push the boundaries of what we can achieve.”

The algorithm outperformed experiments by accurately capturing the ideal distribution of GBS output states, raising questions about the claimed quantum advantage of existing experiments. This insight opens doors for improving the design of future quantum experiments, suggesting that enhancing photon transmission rates and increasing the number of squeezed states could significantly boost their effectiveness.

## Implications for Future Technologies

The implications of these findings extend beyond the realm of quantum computing. As quantum technologies continue to evolve, they hold the potential to revolutionize fields such as cryptography, materials science, and drug discovery. For instance, quantum computing could lead to breakthroughs in secure communication methods, enabling more robust protection of sensitive data. In materials science, quantum simulations can help discover new materials with unique properties, paving the way for advancements in technology, energy storage, and manufacturing. By advancing our understanding of these systems, researchers are laying the groundwork for practical applications that could change the way we approach complex problems in various sectors.

The pursuit of quantum advantage is not just an academic endeavor; it has tangible implications for industries that rely on complex computations. As quantum technologies mature, they have the potential to play a crucial role in optimizing supply chains, enhancing artificial intelligence algorithms, and improving climate modeling. The collaboration between quantum and classical computing is crucial for realizing these advancements, as it allows researchers to harness the strengths of both paradigms.

## A Cumulative Research Effort

Fefferman worked closely with Professor Liang Jiang from the Pritzker School of Molecular Engineering and former postdoc Changhun Oh , currently an Assistant Professor at the Korea Advanced Institute of Science and Technology, on previous work that culminated in this piece of research.

In 2021, they examined the computational power of noisy intermediate-scale quantum (NISQ) devices through lossy boson sampling . The paper revealed that photon loss affects classical simulation costs depending on the number of input photons, which could lead to exponential savings in classical time complexity. Following this, their second paper focused on the impact of noise in experiments designed to demonstrate quantum supremacy, showing that even with significant noise, quantum devices can still produce results that are difficult for classical computers to match. In their third article, they explored Gaussian boson sampling (GBS) by proposing a new architecture that improves programmability and resilience against photon loss, making large scale experiments more feasible. They then introduced a classical algorithm in their fourth paper that generates outcomes closely aligned with ideal boson sampling, enhancing benchmarking techniques and emphasizing the importance of carefully selecting experiment sizes to preserve the quantum signal amidst noise.Finally, in their latest study, they developed quantum-inspired classical algorithms to tackle graph-theoretical problems like finding the densest k-subgraph and the maximum weight clique and a quantum chemistry problem called the molecular vibronic spectra generation . Their findings suggested that the claimed advantages of quantum methods may not be as significant as previously thought, with their classical sampler performing similarly to the Gaussian boson sampler.

## Looking Ahead

The development of the classical simulation algorithm not only enhances our understanding of Gaussian boson sampling experiments but also highlights the importance of continued research in both quantum and classical computing. The ability to simulate GBS more effectively serves as a bridge toward more powerful quantum technologies, ultimately helping us navigate the complexities of modern challenges. As we explore these insights, we move closer to realizing the full potential of quantum technologies, which could lead to innovative solutions that benefit society as a whole. Each step forward in this journey brings us closer to a future where quantum computing plays a vital role in addressing some of the world’s most pressing challenges. With ongoing research and collaboration, the future of quantum computing looks promising, unlocking new realms of possibility for science and society.

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## Professor Fred Chong Named IEEE Fellow

## CUDA-Q Enabled Resource Reduction for Quantum Clustering Algorithms

Quantum computers can use the quantum properties of superposition, entanglement, and interference to generalize learnings and insights from data. Such quantum machine learning (QML) techniques will eventually run on quantum-accelerated supercomputers that combine the processing powers of CPUs, GPUs, and QPUs to solve some of the world’s most complex problems.

Many QML algorithms offer theoretical speedups by assuming that classical data can be efficiently loaded in superposition using so-called quantum random access memory (QRAM). The lack of any efficient means to implement QRAM means that early quantum computers will likely excel at compute , rather than data-intensive tasks.

In practice, QML algorithms that are effective on near and mid-term hardware must focus on compute-intensive heuristics that can analyze data in the absence of QRAM.

This post highlights recent research by Associate Professor Dr Petros Wallden and his team at the Quantum Software Lab, part of the School of Informatics in the University of Edinburgh. Petros is an expert in quantum informatics, with research ranging from quantum algorithms and quantum cryptography to the foundations of quantum informatics.

Petros’ team used the NVIDIA CUDA-Q (formerly CUDA Quantum) platform to develop and accelerate the simulation of new QML methods to significantly reduce the qubit count necessary to study large data sets.

Petros’ team extended Harrow’s work , which uses the concept of coresets to provide a novel way of building realistic oracles for QML applications, without the need for QRAM.

## What are coresets?

A coreset is formed by taking a full data set and optimally mapping it to a smaller weighted data set (Figure 1). The coreset can then be analyzed to approximate traits of the full data set without the need to process the full data set directly.

Coresets are the result of a classical dimensionality reduction method that preprocesses data before a clustering application. By employing coresets, data-intensive QML tasks can be approximated with orders of magnitude fewer qubits and become more realistic applications for near-term quantum computing.

Standard classical coreset construction techniques usually begin with a data set and a target error and then determine the optimal size of the coreset to satisfy this error requirement. Due to experimental constraints, Petros’ team instead chose the coreset size based on the number of qubits that were available. They then assessed the error resulting from this choice following the quantum computations.

## Quantum approaches for clustering with coresets

With input data reduced to the manageably sized coreset, Petros’ team could explore three quantum clustering algorithms.

Clustering is an unsupervised learning technique describing a family of methods that group similar data points in a meaningful way. These groups, or clusters, can then be used for informed decision making in real-world applications, such as determining whether a tumor is malignant or benign.

Petros’s team used CUDA-Q to implement the following clustering techniques:

- Divisive clustering: An approach where coreset points begin in one cluster and are successively bipartitioned until each data point is in its own cluster. In this approach, the process can be stopped at the K th iteration to see how data is divided into K clusters (Figure 2).
- 3-means clustering: The data points are partitioned into K clusters (three, in this case) based on each point’s relationship to K evolving centers-of-mass (centroids). The process ends when the three clusters converge and no longer change with new iterations.
- Gaussian mixture model (GMM) clustering: The distribution of potential coreset points locations is represented as a mixture of K Gaussian distributions. The data is sorted into K sets based on which Gaussian each coreset point most likely came from.

Each of these clustering techniques outputs a set of coresets and a mapping from each point in the original dataset to one of these coresets. The result is an approximate clustering and dimensionality reduction of the initial, large dataset.

By using a variational quantum algorithm (VQA) framework, each technique was expressed in a way that could use a QPU. Petros and team made this possible by deriving a weighted qubit Hamiltonian (inspired by the max cut problem) encoding the respective cost functions for each clustering method described earlier. Having such a Hamiltonian enabled the iterative VQA process to repeatedly call a QPU, real or simulated, to efficiently calculate the cost minimization required in each clustering routine.

## Using CUDA-Q to overcome scalability issues

Exploring the effectiveness of these QML-clustering approaches required the ability to run simulations of how each algorithm would perform.

The NVIDIA CUDA-Q simulation toolkits enabled comprehensive simulations of each clustering method on problem sizes up to 25 qubits. CUDA-Q sped up these simulations by providing easy access to GPU hardware. It also provided out-of-the-box primitives such as hardware-efficient ansatz kernels used to parametrize the Hamiltonian-based optimization process and spin Hamiltonians that were easily adapted to the clustering algorithm cost functions.

In fact, the performing simulations at the scales that Petros’ team presented in their Big data applications on small quantum computers paper is only possible with the GPU-acceleration provided by CUDA-Q.

Initial experiments simulated only 10 qubits on CPU hardware, but memory constraints made this impossible for the 25-qubit experiments of interest. Implementation in CUDA-Q meant that the initial 10-qubit simulation code was also instantly compatible, running without modification when Petros’ team needed to switch out CPU hardware for an NVIDIA DGX H100 GPU system.

This kind of code scalability is a huge advantage. By pooling the memory of multiple GPUs with the NVIDIA mgpu backend (Figure 3), Petros and team have since scaled the simulation even further by changing the backend target, again without having to significantly alter their original simulation code.

According to Boniface Yogendran, the lead developer on this research, “CUDA-Q enabled us to not worry about qubit scalability limitations and be HPC-ready from day one.”

Yogendran’s code can take the work beyond simulation, as CUDA-Q is inherently also QPU-ready, providing support for deployment on all major QPU modalities.

## Value of CUDA-Q simulations

Being able to easily simulate all three clustering algorithms enabled Petros and his team to benchmark each of them against a brute force method, finding the global optimal solution, and a classical heuristic approach known as Lloyd’s algorithm. The results indicated that the quantum algorithms performed best for the GMM ( K =2) and the divisive clustering approaches were comparable to Lloyd’s algorithm.

Based on the success of this work, Petros’ team plans to continue working with NVIDIA to continue developing and scaling new quantum-accelerated supercomputing applications with CUDA-Q.

## Explore CUDA-Q

CUDA-Q enabled Petros and the team to easily develop novel QML implementations and simulate them with accelerated computing. Implementation in CUDA-Q enables the code to be portable for further large-scale simulations or deployment on physical QPUs.

For more information about CUDA-Q quantum or to get started right away, see the Divisive clustering Jupyter notebook that explores the coreset-enabled divisive clustering method described in this post. The tutorial demonstrates how easy it is to scale the code and run a 34-qubit instance using GPUs.

Download CUDA-Q using any of the methods provided in the CUDA-Q Quick Start guide and find other tutorials on the CUDA-Q Tutorials page.

## Related resources

- GTC session: Integrating CUDA Quantum With Quantum Computers
- GTC session: Holistic Approach to Solving Combinatorial Optimization Problems using Quantum Computing
- GTC session: Defining the Quantum-Accelerated Supercomputer
- NGC Containers: CUDA Quantum
- SDK: CUDA Quantum
- Webinar: Accelerating Quantum Finance with NVIDIA cuQuantum and QODA

## IMAGES

## VIDEO

## COMMENTS

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