Many Physicists Believe That Entanglement Is The

NEWS FEATURE SPACE. TIME. ENTANGLEMENT.

n early 2009, determined to make the most annual essay contest run by the Gravity Many physicists believe of his first sabbatical from teaching, Mark Research Foundation in Wellesley, Massachu- Van Raamsdonk decided to tackle one of setts. Not only did he win first prize, but he also that entanglement is Ithe deepest mysteries in physics: the relation- got to savour a particularly satisfying irony: the the essence of quantum ship between quantum mechanics and gravity. honour included guaranteed publication in After a year of work and consultation with col- General Relativity and Gravitation. The journal PICTURES PARAMOUNT weirdness — and some now leagues, he submitted a paper on the topic to published the shorter essay1 in June 2010.

suspect that it may also be the Journal of High Energy Physics. Still, the editors had good reason to be BROS. ENTERTAINMENT/ WARNER In April 2010, the journal sent him a rejec- cautious. A successful unification of quantum the essence of space-time. tion — with a referee’s report implying that mechanics and gravity has eluded physicists Van Raamsdonk, a physicist at the University of for nearly a century. Quantum mechanics gov- British Columbia in Vancouver, was a crackpot. erns the world of the small — the weird realm His next submission, to General Relativity in which an atom or particle can be in many BY RON COWEN and Gravitation, fared little better: the referee’s places at the same time, and can simultaneously report was scathing, and the journal’s editor spin both clockwise and anticlockwise. Gravity asked for a complete rewrite. governs the Universe at large — from the fall But by then, Van Raamsdonk had entered a of an apple to the motion of planets, stars and shorter version of the paper into a prestigious galaxies — and is described by Albert Einstein’s

Black holes such as the one depicted in Interstellar And in the years since, so many have rushed to (2014) can be connected by wormholes. explore this idea that Maldacena’s paper is now one of the most highly cited articles in physics. Einstein loathed the idea of entanglement, Among the enthusiasts was Van Raams- and famously derided it as “spooky action at a donk, who started his sabbatical by pondering distance”. But it is central to quantum theory. one of the central unsolved questions posed And Van Raamsdonk, drawing on work by by Maldacena’s discovery: exactly how does a like-minded physicists going back more than quantum field on the boundary produce grav- a decade, argued for the ultimate irony — that, ity in the bulk? There had already been hints3 despite Einstein’s objections, entanglement that the answer might involve some sort of might be the basis of geometry, and thus of relation between geometry and entanglement. Einstein’s geometric theory of gravity. “Space- But it was unclear how significant these hints time,” he says, “is just a geometrical picture of were: all the earlier work on this idea had dealt how stuff in the quantum system is entangled.” This idea is a long way from being proved, and is hardly a complete theory of quantum gravity. But independent studies have reached “I HAD UNDERSTOOD much the same conclusion, drawing intense interest from major theorists. A small indus- try of physicists is now working to expand the geometry–entanglement relationship, using all SOMETHING THAT the modern tools developed for quantum com- puting and quantum information theory. “I would not hesitate for a minute,” says NO ONE HAD physicist Bartłomiej Czech of Stanford Uni- versity in California, “to call the connections between quantum theory and gravity that have emerged in the last ten years revolutionary.” UNDERSTOOD GRAVITY WITHOUT GRAVITY Much of this work rests on a discovery2 BEFORE.” announced in 1997 by physicist Juan Maldacena, now at the Institute for Advanced with special cases, such as a bulk universe that Study in Princeton, New Jersey. Maldacena’s contained a black hole. So Van Raamsdonk research had led him to consider the relation- decided to settle the matter, and work out ship between two seemingly different model whether the relationship was true in general, universes. One is a cosmos similar to our own. or was just a mathematical oddity. Although it neither expands nor contracts, it He first considered an empty bulk universe, has three dimensions, is filled with quantum which corresponded to a single quantum field particles and obeys Einstein’s equations of grav- on the boundary. This field, and the quan- ity. Known as anti-de Sitter space (AdS), it is tum relationships that tied various parts of it commonly referred to as the bulk. The other together, contained the only entanglement in model is also filled with elementary particles, the system. But now, Van Raamsdonk won- but it has one dimension fewer and doesn’t dered, what would happen to the bulk universe recognize gravity. Commonly known as the if that boundary entanglement were removed? boundary, it is a mathematically defined mem- He was able to answer that question using brane that lies an infinite distance from any mathematical tools4 introduced in 2006 by given point in the bulk, yet completely encloses Shinsei Ryu, now at the University of Illinois general theory of relativity, announced 100 years it, much like the 2D surface of a balloon enclos- at Urbana–Champaign, and Tadashi Takanagi, ago this month. The theory holds that gravity is ing a 3D volume of air. The boundary particles now at the Yukawa Institute for Theoretical geometry: particles are deflected when they pass obey the equations of a quantum system known Physics at Kyoto University in Japan. Their near a massive object not because they feel a as conformal field theory (CFT). equations allowed him to model a slow and force, said Einstein, but because space and time Maldacena discovered that the boundary methodical reduction in the boundary field’s around the object are curved. and the bulk are completely equivalent. Like entanglement, and to watch the response in Both theories have been abundantly verified the 2D circuitry of a computer chip that the bulk, where he saw space-time steadily through experiment, yet the realities they encodes the 3D imagery of a computer game, elongating and pulling apart (see ‘The entan- describe seem utterly incompatible. And from the relatively simple, gravity-free equations glement connection’). Ultimately, he found, the editors’ standpoint, Van Raamsdonk’s that prevail on the boundary contain the same reducing the entanglement to zero would approach to resolving this incompatibility was information and describe the same physics as break the space-time into disjointed chunks, strange. All that’s needed, he asserted, is ‘entan- the more complex equations that rule the bulk. like chewing gum stretched too far. glement’: the phenomenon that many physicists “It’s kind of a miraculous thing,” says Van The geometry–entanglement relationship believe to be the ultimate in quantum weirdness. Raamsdonk. Suddenly, he says, Maldacena’s was general, Van Raamsdonk realized. Entan- Entanglement lets the measurement of one duality gave physicists a way to think about glement is the essential ingredient that knits particle instantaneously determine the state of quantum gravity in the bulk without thinking space-time together into a smooth whole — not a partner particle, no matter how far away it may about gravity at all: they just had to look at the just in exotic cases with black holes, but always. be — even on the other side of the Milky Way. equivalent quantum state on the boundary. “I felt that I had understood something

19 NOVEMBER 2015 | VOL 527 | NATURE | 291 © 2016 Macmillan Publishers Limited. All rights reserved THE ENTANGLEMENT CONNECTION The ghostly quantum phenomenon of entanglement may be what knits space-time into a smooth whole.

In an in nite model universe known as about a fundamental question that perhaps anti -de Sitter space, the eects of gravity at ry nobody had understood before,” he recalls: NATURE a any point x in the interior are mathematically d n equivalent to a quantum eld theory on its u x “Essentially, what is space-time?” o B boundary. This universe can be visuali z ed in

2D by lling it with imaginary triangles. ENTANGLEMENT AND EINSTEIN Anti-de Sitter Although the triangles are identical, they look NIK SPENCER/ space increasingly distorted as they approach the Quantum entanglement as geometric glue — boundary. this was the essence of Van Raamsdonk’s rejected paper and winning essay, and an idea Physicists noticed that this pattern that has increasingly resonated among physi- resembled diagrams called tensor networks, which were invented to show cists. No one has yet found a rigorous proof, so Tensor connections between quantum particles s the idea still ranks as a conjecture. But many le on a massive scale. These connections network ic t r independent lines of reasoning support it. are known as quantum entanglement . a p In 2013, for example Maldacena and Leonard ed gl 5 an Susskind of Stanford published a related con- nt What is quantum entanglement? E jecture that they dubbed ER = EPR, in honour In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen (EPR) pointed out that a connection can exist of two landmark papers from 1935. ER, by Ein- between widely separated quantum systems: a measurement of one will determine the state of the other. stein and American-Israeli physicist Nathan 6 EXAMPLE Entangled spins: The Observation of Rosen, introduced what is now called a worm- if one particle is particles are one particle hole: a tunnel through space-time connecting spinning up, the separated. instantaneously two black holes. (No real particle could actually other spins down, reveals the state and vice versa. of the other. travel through such a wormhole, science-fic- tion films notwithstanding: that would require moving faster than light, which is impossible.) DISENTANGLEMENT EPR, by Einstein, Rosen and American physi- The bulk–boundary correspondence cist Boris Podolsky, was the first paper to clearly implies that space on the inside is built from articulate what is now called entanglement7. quantum entanglement around the outside. Maldacena and Susskind’s conjecture was that these two concepts are related by more Empty Even when the bulk universe is empty, A space B than a common publication date. If any two the quantum elds in any two regions of the boundary (A and B) are heavily particles are connected by entanglement, the entangled with one another. physicists suggested, then they are effectively joined by a wormhole. And vice versa: the connection that physicists call a wormhole is equivalent to entanglement. They are different ways of describing the same underlying reality. If the entanglement No one has a clear idea of what this under between these regions is reduced, lying reality is. But physicists are increasingly the bulk universe A B convinced that it must exist. Maldacena, starts pulling Susskind and others have been testing the apart. ER = EPR hypothesis to see if it is mathematically consistent with everything else that is known about entanglement and wormholes — and so far, the answer is yes. When the entanglement is reduced to zero, HIDDEN CONNECTIONS the bulk universe Other lines of support for the geometry– splits in two — A B showing that entanglement relationship have come from entanglement condensed-matter physics and quantum infor- is necessary for mation theory: fields in which entanglement space to exist. already plays a central part. This has allowed researchers from these disciplines to attack quantum gravity with a whole array of fresh concepts and mathematical tools. ER = EPR Tensor networks, for example, are a technique Also in 1935, Einstein and Rosen (ER) showed that widely developed by condensed-matter physicists to Wormhole separated black holes can be track the quantum states of huge numbers of Black Black connected by a tunnel through hole 1 hole 2 subatomic particles. Brian Swingle was using space-time now often known as a wormhole. them in this way in 2007, when he was a gradu- ate student at the Massachusetts Institute of Technology (MIT) in Cambridge, calculating Physicists suspect that the how groups of electrons interact in a solid mat connection in a wormhole and the erial. He found that the most useful network for connection in quantum entanglement are the same thing, just on a Quantum this purpose started by linking adjacent pairs entanglement vastly di erent scale. of electrons, which are most likely to interact Aside from their size there is Particle Particle with each other, then linking larger and larger no fundamental dierence. 1 2 groups in a pattern that resembled the hierarchy

292 | NATURE | VOL 527 | 19 NOVEMBER 2015 © 2016 Macmillan Publishers Limited. All rights reserved FEATURE NEWS of a family tree. But then, during a course in saying for years that entanglement is somehow number that would take aeons to compute. quantum field theory, Swingle learned about important for the emergence of the bulk,” says Susskind’s road to computational complex- Maldacena’s bulk–boundary correspondence Harlow. “But for the first time, I think we are ity began about a decade ago, when he noticed and noticed an intriguing pattern: the mapping really getting a glimpse of how and why.” that a solution to Einstein’s equations of gen- between the bulk and the boundary showed eral relativity allowed a wormhole in AdS space exactly the same tree-like network. BEYOND ENTANGLEMENT to get longer and longer as time went on. What Swingle wondered whether this resemblance That prospect seems to be enticing for the did that correspond to on the boundary, he might be more than just coincidence. And in Simons Foundation, a philanthropic organiza- wondered? What was changing there? Suss- 2012, he published8 calculations showing that tion in New York City that announced in August kind knew that it couldn’t be entanglement, it was: he had independently reached much the that it would provide US$2.5 million per year because the correlations that produce entan- same conclusion as Van Raamsdonk, thereby for at least 4 years to help researchers to move glement between different particles on the adding strong support to the geometry–entan- forward on the gravity–quantum information boundary reach their maximum in less than glement idea. “You can think of space as being connection. “Information theory provides a a second10. In an article last year11, however, built from entanglement in this very precise way powerful way to structure our thinking about he and Douglas Stanford, now at the Institute using the tensors,” says Swingle, who is now at fundamental physics,” says Patrick Hayden, for Advanced Study, showed that as time pro- Stanford and has seen tensor networks become the Stanford physicist who is directing the pro- gressed, the quantum state on the boundary a frequently used tool to explore the geometry– gramme. He adds that the Simons sponsorship would vary in exactly the way expected from entanglement correspondence. computational complexity. Another prime example of cross-fertilization “It appears more and more that the growth of is the theory of quantum error-correcting codes, the interior of a black hole is exactly the growth which physicists invented to aid the construc- “YOU CAN THINK of computational complexity,” says Susskind. If tion of quantum computers. These machines quantum entanglement knits together pieces of encode information not in bits but in ‘qubits’: space, he says, then computational complexity quantum states, such as the up or down spin of may drive the growth of space — and thus bring an electron, that can take on values of 1 and 0 OF SPACE AS in the elusive element of time. One potential simultaneously. In principle, when the qubits consequence, which he is just beginning to interact and become entangled in the right explore, could be a link between the growth of way, such a device could perform calculations BEING BUILT FROM computational complexity and the expansion that an ordinary computer could not finish in of the Universe. Another is that, because the the lifetime of the Universe. But in practice, the insides of black holes are the very regions where process can be incredibly fragile: the slightest ENTANGLEMENT.” quantum gravity is thought to dominate, com- disturbance from the outside world will disrupt putational complexity may have a key role in a the qubits’ delicate entanglement and destroy complete theory of quantum gravity. any possibility of quantum computation. will support 16 main researchers at 14 institu- Despite the remaining challenges, there is a That need inspired quantum error-correcting tions worldwide, along with students, postdocs sense among the practitioners of this field that codes, numerical strategies that repair cor- and a series of workshops and schools. Ulti- they have begun to glimpse something real and rupted correlations between the qubits and mately, one major goal is to build up a compre- very important. “I didn’t know what space was make the computation more robust. One hensive dictionary for translating geometric made of before,” says Swingle. “It wasn’t clear hallmark of these codes is that they are always concepts into quantum language, and vice versa. that question even had meaning.” But now, ‘non-local’: the information needed to restore This will hopefully help physicists to find their he says, it is becoming increasingly apparent any given qubit has to be spread out over a wide way to the complete theory of quantum gravity. that the question does make sense. “And the region of space. Otherwise, damage in a single Still, researchers face several challenges. answer is something that we understand,” says spot could destroy any hope of recovery. And One is that the bulk–boundary correspond- Swingle. “It’s made of entanglement.” that non-locality, in turn, accounts for the fas- ence does not apply in our Universe, which As for Van Raamsdonk, he has written some cination that many quantum information theo- is neither static nor bounded; it is expanding 20 papers on quantum entanglement since rists feel when they first encounter Maldacena’s and apparently infinite. Most researchers in the 2009. All of them, he says, have been accepted bulk–boundary correspondence: it shows a very field do think that calculations using Malda- for publication. ■ similar kind of non-locality. The information cena’s correspondence are telling them some- that corresponds to a small region of the bulk is thing true about the real Universe, but there is Ron Cowen is a freelance writer based in spread over a vast region of the boundary. little agreement as yet on exactly how to trans- Silver Spring, Maryland. “Anyone could look at AdS–CFT and say late results from one regime to the other. 1. Van Raamsdonk, M. Gen. Relativ. Grav. 42, that it’s sort of vaguely analogous to a quantum Another challenge is that the standard 2323–2329 (2010). error-correcting code,” says Scott Aaronson, a definition of entanglement refers to particles 2. Maldacena, J. M. Adv. Theor. Math. Phys. 2, 231–252 (1998). computer scientist at MIT. But in work pub- only at a given moment. A complete theory of 3. Maldacena, J. M. J. High Energy Phys. 2003, 021 9 lished in June , physicists led by Daniel Harlow quantum gravity will have to add time to that (2003). at Harvard University in Cambridge and John picture. “Entanglement is a big piece of the 4. Ryu, S. & Takayanagi, T. Phys. Rev. Lett. 96, 181602 (2006). Preskill of the California Institute of Technol- story, but it’s not the whole story,” says Susskind. 5. Maldacena, J. & Susskind, L. Fortschr. Phys. 61, ogy in Pasadena argue for something stronger: He thinks physicists may have to embrace 781–811 (2013). 6. Einstein, A. & Rosen, N. Phys. Rev. 48, 73–77 that the Maldacena duality is itself a quantum another concept from quantum information (1935). error-correcting code. They have demonstrated theory: computational complexity, the number 7. Einstein, A., Podolsky, B. & Rosen, N. Phys. Rev. 47, that this is mathemati- of logical steps, or operations, needed to con- 777–780 (1935). 8. Swingle, B. Phys. Rev. D 86, 065007 (2012). cally correct in a simple NATURE.COM struct the quantum state of a system. A system 9. Pastawski, F. et al. J. High Energy Phys. 2015, 149 model, and are now try- For more on general with low complexity is analogous to a quantum (2015). ing to show that the asser- relativity at 100. computer with almost all the qubits on zero: it is 10. Susskind, L. Preprint at http://arxiv.org/ abs/1411.0690 (2014). tion holds more generally. nature.com/ easy to define and to build. One with high com- 11. Stanford, D. & Susskind, L. Phys. Rev. D 90, 126007 “People have been relativity100 plexity is analogous to a set of qubits encoding a (2014).

CORRECTED 23 DECEMBER 2015 | 19 NOVEMBER 2015 | VOL 527 | NATURE | 293 © 2016 Macmillan Publishers Limited. All rights reserved CORRECTION The News Feature ‘Space. Time. Entanglement.’ (Nature 527, 290–293; 2015) wrongly said that Leonard Susskind began to think about computational complexity ten years ago — his work in the area began around three years ago.