Entanglement = Wormholes

One of the most enjoyable and inspiring physics papers I have read in recent years is this one by Mark Van Raamsdonk. Building on earlier observations by Maldacena and by Ryu and Takayanagi. Van Raamsdonk proposed that quantum entanglement is the fundamental ingredient underlying spacetime geometry.* Since my first encounter with this provocative paper, I have often mused that it might be a Good Thing for someone to take Van Raamsdonk’s idea really seriously.

Now someone has.

I love wormholes. (Who doesn’t?) Picture two balls, one here on earth, the other in the Andromeda galaxy. It’s a long trip from one ball to the other on the background space, but there’s a shortcut:You can walk into the ball on earth and moments later walk out of the ball in Andromeda. That’s a wormhole.

I’ve mentioned before that John Wheeler was one of my heros during my formative years. Back in the 1950s, Wheeler held a passionate belief that “everything is geometry,” and one particularly intriguing idea he called “charge without charge.” There are no pointlike electric charges, Wheeler proclaimed; rather, electric field lines can thread the mouth of a wormhole. What looks to you like an electron is actually a tiny wormhole mouth. If you were small enough, you could dive inside the electron and emerge from a positron far away. In my undergraduate daydreams, I wished this idea could be true.

But later I found out more about wormholes, and learned about “topological censorship.” It turns out that if energy is nonnegative, Einstein’s gravitational field equations prevent you from traversing a wormhole — the throat always pinches off (or becomes infinitely long) before you get to the other side. It has sometimes been suggested that quantum effects might help to hold the throat open (which sounds like a good idea for a movie), but today we’ll assume that wormholes are never traversable no matter what you do.

Alice and Bob are in different galaxies, but each lives near a black hole, and their black holes are connected by a wormhole.

Love in a wormhole throat: Alice and Bob are in different galaxies, but each lives near a black hole, and their black holes are connected by a wormhole. If both jump into their black holes, they can enjoy each other’s company for a while before meeting a tragic end.

Are wormholes any fun if we can never traverse them? The answer might be yes if two black holes are connected by a wormhole. Then Alice on earth and Bob in Andromeda can get together quickly if each jumps into a nearby black hole. For solar mass black holes Alice and Bob will have only 10 microseconds to get acquainted before meeting their doom at the singularity. But if the black holes are big enough, Alice and Bob might have a fulfilling relationship before their tragic end.

This observation is exploited in a recent paper by Juan Maldacena and Lenny Susskind (MS) in which they reconsider the AMPS puzzle (named for Almheiri, Marolf, Polchinski, and Sully). I wrote about this puzzle before, so I won’t go through the whole story again. Here’s the short version: while classical correlations can easily be shared by many parties, quantum correlations are harder to share. If Bob is highly entangled with Alice, that limits his ability to entangle with Carrie, and if he entangles with Carrie instead he can’t entangle with Alice. Hence we say that entanglement is “monogamous.” Now, if, as most of us are inclined to believe, information is “scrambled” but not destroyed by an evaporating black hole, then the radiation emitted by an old black hole today should be highly entangled with radiation emitted a long time ago. And if, as most of us are inclined to believe, nothing unusual happens (at least not right away) to an observer who crosses the event horizon of a black hole, then the radiation emitted today should be highly entangled with stuff that is still inside the black hole. But we can’t have it both ways without violating the monogamy of entanglement!

The AMPS puzzle invites audacious reponses, and AMPS were suitably audacious. They proposed that an old black hole has no interior — a freely falling observer meets her doom right at the horizon rather than at a singularity deep inside.

MS are also audacious, but in a different way. They helpfully summarize their key point succinctly in a simple equation:


Here, EPR means Einstein-Podolsky-Rosen, whose famous paper highlighted the weirdness of quantum correlations, while ER means Einstein-Rosen (sorry, Podolsky), who discovered wormhole solutions to the Einstein equations. (Both papers were published in 1935.) MS (taking Van Raamsdonk very seriously) propose that whenever any two quantum subsystems are entangled they are connected by a wormhole. In many cases, these wormholes are highly quantum mechanical, but in some cases (where the quantum system under consideration has a weakly coupled “gravitational dual”), the wormhole can have a smooth geometry like the one ER described. That wormholes are not traversable is important for the consistency of ER = EPR: just as Alice cannot use their shared entanglement to send a message to Bob instantaneously, so she is unable to send Bob a message through their shared wormhole.

AMPS imagined that Alice could distill qubit C from the black hole’s early radiation and carry it back to the black hole, successfully verifying its entanglement with another qubit B distilled from the recent radiation. Monogamy then ensures that qubit B cannot be entangled with qubit A behind the horizon. Hence when Alice falls through the horizon she will not observe the quiescent vacuum state in which A and B are entangled; instead she encounters a high-energy particle. MS agree with this conclusion.

AMPS go on to say that Alice’s actions before entering the black hole could not have created that energetic particle; it must have been there all along, one of many such particles constituting a seething firewall.

Here MS disagree. They argue that the excitation encountered by Alice as she crosses the horizon was actually created by Alice herself when she interacted with qubit C. How could Alice’s actions, executed far, far away from the black hole, dramatically affect the state of the black hole’s interior? Because C and A are connected by a wormhole!

The ER = EPR conjecture seems to allow us to view the early radiation with which the black hole is entangled as a complementary description of the black hole interior. It’s not clear yet whether this picture works in detail, and even if it does there could still be firewalls; maybe in some sense the early radiation is connected to the black hole via a wormhole, yet this wormhole is wildly fluctuating rather than a smooth geometry. Still, MS provide a promising new perspective on a deep problem.

As physicists we often rely on our sense of smell in judging scientific ideas, and earlier proposed resolutions of the AMPS puzzle (like firewalls) did not smell right. At first whiff, ER = EPR may smell fresh and sweet, but it will have to ripen on the shelf for a while. If this idea is on the right track, there should be much more to say about it. For now, wormhole lovers can relish the possibilities.

Eventually, Wheeler discarded “everything is geometry” in favor of an ostensibly deeper idea: “everything is information.” It would be a fitting vindication of Wheeler’s vision if everything in the universe, including wormholes, is made of quantum correlations.

*Update: Commenter JM reminded me to mention Brian Swingle’s beautiful 2009 paper, which preceded Van Raamsdonk’s and proposed a far-reaching connection between quantum entanglement and spacetime geometry.

A Public Lecture on Quantum Information

Sooner or later, most scientists are asked to deliver a public lecture about their research specialties. When successful, lecturing about science to the lay public can give one a feeling of deep satisfaction. But preparing the lecture is a lot of work!

Caltech sponsors the Earnest C. Watson lecture series (named after the same Earnest Watson mentioned in my post about Jane Werner Watson), which attracts very enthusiastic audiences to Beckman Auditorium nine times a year. I gave a Watson lecture on April 3 about Quantum Entanglement and Quantum Computing, which is now available from iTunes U and also on YouTube:

I did a Watson lecture once before, in 1997. That occasion precipitated some big changes in my presentation style. To prepare for the lecture, I acquired my first laptop computer and learned to use PowerPoint. This was still the era when a typical physics talk was handwritten on transparencies and displayed using an overhead projector, so I was sort of a pioneer. And I had many anxious moments in the late 1990s worrying about whether my laptop would be able to communicate with the projector — that can still be a problem even today, but was a more common problem then.

I invested an enormous amount of time in preparing that 1997 lecture, an investment still yielding dividends today. Aside from figuring out what computer to buy (an IBM ThinkPad) and how to do animation in PowerPoint, I also learned to draw using Adobe Illustrator under the tutelage of Caltech’s digital media expert Wayne Waller. And apart from all that technical preparation, I had to figure out the content of the lecture!

That was when I first decided to represent a qubit as a box with two doors, which contains a ball that can be either red or green, and I still use some of the drawings I made then.

Entanglement, illustrated with balls in boxes.

Entanglement, illustrated with balls in boxes.

This choice of colors was unfortunate, because people with red-green color blindness cannot tell the difference. I still feel bad about that, but I don’t have editable versions of the drawings anymore, so fixing it would be a big job …

I also asked my nephew Ben Preskill (then 10 years old, now a math PhD candidate at UC Berkeley), to make a drawing for me illustrating weirdness.

The desire to put weirdness to work has driven the emergence of quantum information science.

The desire to put weirdness to work has driven the emergence of quantum information science.

I still use that, for sentimental reasons, even though it would be easier to update.

The turnout at the lecture was gratifying (you can’t really see the audience with the spotlight shining in your eyes, but I sensed that the main floor of the Auditorium was mostly full), and I have gotten a lot of positive feedback (including from the people who came up to ask questions afterward — we might have been there all night if the audio-visual staff had not forced us to go home).

I did make a few decisions about which I have had second thoughts. I was told I had the option of giving a 45 minute talk with a public question period following, or a 55 minute talk with only a private question period, and I opted for the longer talk. Maybe I should have pushed back and insisted on allowing some public questions even after the longer talk — I like answering questions. And I was told that I should stay in the spotlight, to ensure good video quality, so I decided to stand behind the podium the whole time to curb my tendency to pace across the stage. But maybe I would have seemed more dynamic if I had done some pacing.

I got some gentle criticism from my wife, Roberta, who suggested I could modulate my voice more. I have heard that before, particularly in teaching evaluations that complain about my “soporific” tone. I recall that Mike Freedman once commented after watching a video of a public lecture I did at the KITP in Santa Barbara — he praised its professionalism and “newscaster quality”. But that cuts two ways, doesn’t it? Paul Ginsparg listened to a podcast of that same lecture while doing yardwork, and then sent me a compliment by email, with a characteristic Ginspargian twist. Noting that my sentences were clear, precise, and grammatical, Paul asked: “is this something that just came naturally at some early age, or something that you were able to acquire at some later stage by conscious design (perhaps out of necessity, talks on quantum computing might not go over as well without the reassuring smoothness)?”

Another criticism stung more. To illustrate the monogamy of entanglement, I used a slide describing the frustration of Bob, who wants to entangle with both Alice and Carrie, but finds that he can increase his entanglement with Carrie only my sacrificing some of his entanglement with Alice.

Entanglement is monogamous. Bob is frustrated to find that he cannot be fully entangled with both Alice and Carrie.

Entanglement is monogamous. Bob is frustrated to find that he cannot be fully entangled with both Alice and Carrie.

This got a big laugh. But I used the same slide in a talk at the APS Denver meeting the following week (at a session celebrating the 100th anniversary of Niels Bohr’s atomic model), and a young woman came up to me after that talk to complain. She suggested that my monogamy metaphor was offensive and might discourage women from entering the field!

After discussing the issue with Roberta, I decided to address the problem by swapping the gender roles. The next day, during the question period following Stephen Hawking’s Public Lecture, I spoke about Betty’s frustration over her inability to entangle fully with both Adam and Charlie. But is that really an improvement, or does it reflect negatively on Betty’s morals? I would appreciate advice about this quandary in the comments.

In case you watch the video, there are a couple of things you should know. First, in his introduction, Tom Soifer quotes from a poem about me, but neglects to name the poet. It is former Caltech postdoc Patrick Hayden. And second, toward the end of the lecture I talk about some IQIM outreach activities, but neglect to name our Outreach Director Spiros Michalakis, without whose visionary leadership these things would not have happened.

The most touching feedback I received came from my Caltech colleague Oskar Painter. I joked in the lecture about how mild mannered IQIM scientists can unleash the superpower of quantum information at a moment’s notice.

Mild mannered professor unleashes the super power of quantum information.

Mild mannered professor unleashes the superpower of quantum information.

After watching the video, Oskar shot me an email:

“I sent a link to my son [Ewan, age 11] and daughter [Quinn, age 9], and they each watched it from beginning to end on their iPads, without interruption.  Afterwards, they had a huge number of questions for me, and were dreaming of all sorts of “quantum super powers” they imagined for the future.”

Jeff Kimble stands tall

Jeff Kimble played college basketball. I conjecture that he is more than two meters tall, though being a theorist I have never measured him. Jeff certainly stands tall in the Pantheon of outstanding physicists, and we at Quantum Frontiers were thrilled to hear that Jeff has received the 2013 Herbert Walther Award, which is very well deserved.

About four years ago, Jeff gave a public lecture at Caltech about “The Quantum Internet,” and I had the honor of introducing him. The video of Jeff’s lecture and my introduction are available for free at iTunes U, or by clicking on the embedded video below. You’ll have to watch the video to hear all the Buddy Holly references in my introduction (Jeff and Buddy come from the same county in Texas). Jeff’s lecture was memorable, too, featuring a dance performance by his research group.

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Is Alice burning? The black hole firewall controversy

Quantum correlations are monogamous. Bob can be highly entangled with Alice or with Carrie, but not both.

Quantum correlations are monogamous. Bob can be highly entangled with Alice or with Carrie, but not both.

Back in the early 1990s, I was very interested in the quantum physics of black holes and devoted much of my research effort to thinking about how black holes process quantum information. That effort may have prepared me to appreciate Peter Shor’s spectacular breakthrough — the discovery of a quantum algorithm for factoring intergers efficiently. I told the story here of how I secretly struggled to understand Shor’s algorithm while attending a workshop on black holes in 1994.

Since the mid-1990s, quantum information has been the main focus of my research. I hope that some of the work I’ve done can help to hasten the onset of a new era in which quantum computers are used routinely to perform super-classical tasks. But I have always had another motivation for working on quantum information science — a conviction that insights gained by thinking about quantum computation can illuminate deep issues in other areas of physics, especially quantum condensed matter and quantum gravity. In recent years quantum information concepts have begun penetrating into other fields, and I expect that trend to continue.
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How to build a teleportation machine: Intro to qubits

A match made in heaven.

If a tree falls in a forest, and nobody is there to hear it, does it make a sound? The answer was obvious to my 12-year-old self — of course it made a sound. More specifically, something ranging from a thud to a thump. There doesn’t need to be an animal present for the tree to jiggle air molecules. Classical physics for the win! Around the same time I was exposed to this thought experiment, I read Michael Crichton’s Timeline. The premise is simple, but not necessarily feasible: archeologists use ‘quantum technology’ (many-worlds interpretation and quantum teleportation) to travel to the Dordogne region of France in the mid 1300s. Blood, guts, action, drama, and plot twists ensue. I haven’t returned to this book since I was thirteen, so I’m guaranteed to have the plot wrong, but for better or worse, I credit this book with planting the seeds of a misconception about what ‘quantum teleportation’ actually entails. This is the first of a multi-part post which will introduce readers to the one-and-only way we know of how teleportation works.
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