Guns versus butter in quantum information

From my college’s computer-science club, I received a T-shirt that reads:

while(not_dead){

sleep--;

time--;

awesome++;

}

/*There’s a reason we can’t hang out with you…*/

The message is written in Java, a programming language. Even if you’ve never programmed, you likely catch the drift: CS majors are the bees’ knees because, at the expense of sleep and social lives, they code. I disagree with part of said drift: CS majors hung out with me despite being awesome.

photo-3 copy

The rest of the drift—you have to give some to get some—synopsizes the physics I encountered this fall. To understand tradeoffs, you needn’t study QI. But what trades off with what, according to QI, can surprise us.

The T-shirt haunted me at the University of Nottingham, where researchers are blending QI with Einstein’s theory of relativity. Relativity describes accelerations, gravity, and space-time’s curvature. In other sources, you can read about physicists’ attempts to unify relativity and quantum mechanics, the Romeo and Tybalt of modern physics, into a theory of quantum gravity. In this article, relativity tangos with quantum mechanics in relativistic quantum information (RQI). If I move my quantum computer, RQIers ask, how do I change its information processing? How does space-time’s curvature affect computation? How can motion affect measurements?

Answers to these questions involve tradeoffs.

Nottingham

Nottingham researchers kindly tolerating a seminar by me

For example, acceleration entangles particles. Decades ago, physicists learned that acceleration creates particles. Say you’re gazing into a vacuum—not empty space, but nearly empty space, the lowest-energy system that can exist. Zooming away on a rocket, I accelerate relative to you. From my perspective, more particles than you think—and higher-energy particles—surround us.

Have I created matter? Have I violated the Principle of Conservation of Energy (and Mass)? I created particles in a sense, but at the expense of rocket fuel. You have to give some to get some:

Fuel--;
Particles++;

The math that describes my particles relates to the math that describes entanglement.* Entanglement is a relationship between quantum systems. Say you entangle two particles, then separate them. If you measure one, you instantaneously affect the other, even if the other occupies another city.

Say we encode information in quantum particles stored in a box.** Just as you encode messages by writing letters, we write messages in the ink of quantum particles. Say the box zooms off on a rocket. Just as acceleration led me to see particles in a vacuum, acceleration entangles the particles in our box. Since entanglement facilitates computation, you can process information by shaking a box. And performing another few steps.

When an RQIer told me so, she might as well have added that space-time has 106 dimensions and the US would win the World Cup. Then my T-shirt came to mind. To get some, you have to give some. When you give something, you might get something. Giving fuel gets you entanglement. To prove that statement, I need to do and interpret math. Till I have time to,

Fuel--;
Entanglement++;

offers intuition.

After cropping up in Nottingham, my T-shirt reared its head (collar?) in physics problem after physics problem. By “consuming entanglement”—forfeiting that ability to affect the particle in another city—you can teleport quantum information.

Entanglement--;
Quantum teleportation++;

My research involves tradeoffs between information and energy. As the Hungarian physicist Leó Szilárd showed, you can exchange information for work. Say you learn which half of a box*** a particle occupies, and you trap the particle in that half. Upon freeing the particle—forfeiting your knowledge about its location—you can lift a weight, charge a battery, or otherwise store energy.

Information--;
Energy++;

If you expend energy, Rolf Landauer showed, you can gain knowledge.

Energy--;
Information++;

No wonder my computer-science friends joked about sleep deprivation. But information can energize. For fuel, I forage in the blending of fields like QI and relativity, and in physical intuitions like those encapsulated in the pseudo-Java above. Much as Szilard’s physics enchants me, I’m glad that the pursuit of physics contradicts his conclusion:

while(not_dead){

Information++;

Energy++;

}

The code includes awesome++ implicitly.

*Bogoliubov transformations, to readers familiar with the term.

**In the fields in a cavity, to readers familiar with the terms.

***Physicists adore boxes, you might have noticed.

With thanks to Ivette Fuentes and the University of Nottingham for their hospitality and for their introduction to RQI.

Making predictions in the multiverse

Image

I am a theoretical physicist at University of California, Berkeley. Last month, I attended a very interesting conference organized by Foundamental Questions Institute (FQXi) in Puerto Rico, and presented a talk about making predictions in cosmology, especially in the eternally inflating multiverse. I very much enjoyed discussions with people at the conference, where I was invited to post a non-technical account of the issue as well as my own view of it. So here I am.

I find it quite remarkable that some of us in the physics community are thinking with some “confidence” that we live in the multiverse, more specifically one of the many universes in which low-energy physical laws take different forms. (For example, these universes have different elementary particles with different properties, possibly different spacetime dimensions, and so on.) This idea of the multiverse, as we currently think, is not simply a result of random imagination by theorists, but is based on several pieces of observational and theoretical evidence.

Observationally, we have learned more and more that we live in a highly special universe—it seems that the “physical laws” of our universe (summarized in the form of standard models of particle physics and cosmology) takes such a special form that if its structure were varied slightly, then there would be no interesting structure in the universe, let alone intelligent life. It is hard to understand this fact unless there are many universes with varying “physical laws,” and we simply happen to emerge in a universe which allows for intelligent life to develop (which seems to require special conditions). With multiple universes, we can understand the “specialness” of our universe precisely as we understand the “specialness” of our planet Earth (e.g. the ideal distance from the sun), which is only one of the many planets out there.

Perhaps more nontrivial is the fact that our current theory of fundamental physics leads to this picture of the multiverse in a very natural way. Imagine that at some point in the history of the universe, space is exponentially expanding. This expansion—called inflation—occurs when space is filled with a “positive vacuum energy” (which happens quite generally). We knew, already in 80’s, that such inflation is generically eternal. During inflation, various non-inflating regions called bubble universes—of which our own universe could be one—may form, much like bubbles in boiling water. Since ambient space expands exponentially, however, these bubbles do not percolate; rather, the process of creating bubble universes lasts forever in an eternally inflating background. Now, recent progress in string theory suggests that low energy theories describing phyics in these bubble universes (such as the elementary particle content and their properties) may differ bubble by bubble. This is precisely the setup needed to understand the “specialness” of our universe because of the selection effect associated with our own existence, as described above.

multiverse

A schematic depiction of the eternally inflating multiverse. The horizontal and vertical directions correspond to spatial and time directions, respectively, and various regions with the inverted triangle or argyle shape represent different universes. While regions closer to the upper edge of the diagram look smaller, it is an artifact of the rescaling made to fit the large spacetime into a finite drawing—the fractal structure near the upper edge actually corresponds to an infinite number of large universes.

This particular version of the multiverse—called the eternally inflating multiverse—is very attractive. It is theoretically motivated and has a potential to explain various features seen in our universe. The eternal nature of inflation, however, causes a serious issue of predictivity. Because the process of creating bubble universes occurs infinitely many times, “In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times,” as phrased in an article by Alan Guth. Suppose we want to calculate the relative probability for (any) events A and B to happen in the multiverse. Following the standard notion of probability, we might define it as the ratio of the numbers of times events A and B happen throughout the whole spacetime

P = \frac{N_A}{N_B}.

In the eternally inflating multiverse, however, both A and B occur infinitely many times: N_A, N_B = \infty. This expression, therefore, is ill-defined. One might think that this is merely a technical problem—we simply need to “regularize” to make both N_{A,B} finite, at a middle stage of the calculation, and then we get a well-defined answer. This is, however, not the case. One finds that depending on the details of this regularization procedure, one can obtain any “prediction” one wants, and there is no a priori preferred way to proceed over others—predictivity of physical theory seems lost!

Over the past decades, some physicists and cosmologists have been thinking about many aspects of this so-called measure problem in eternal inflation. (There are indeed many aspects to the problem, and I’m omitting most of them in my simplified presentation above.) Many of the people who contributed were in the session at the conference, including Aguirre, Albrecht, Bousso, Carroll, Guth, Page, Tegmark, and Vilenkin. My own view, which I think is shared by some others, is that this problem offers a window into deep issues associated with spacetime and gravity. In my 2011 paper I suggested that quantum mechanics plays a crucial role in understanding the multiverse, even at the largest distance scales. (A similar idea was also discussed here around the same time.) In particular, I argued that the eternally inflating multiverse and quantum mechanical many worlds a la Everett are the same concept:

Multiverse = Quantum Many Worlds

in a specific, and literal, sense. In this picture, the global spacetime of general relativity appears only as a derived concept at the cost of overcounting true degrees of freedom; in particular, infinitely large space associated with eternal inflation is a sort of “illusion.” A “true” description of the multiverse must be “intrinsically” probabilistic in a quantum mechanical sense—probabilities in cosmology and quantum measurements have the same origin.

To illustrate the basic idea, let us first consider an (apparently unrelated) system with a black hole. Suppose we drop some book A into the black hole and observe subsequent evolution of the system from a distance. The book will be absorbed into (the horizon of) the black hole, which will then eventually evaporate, leaving Hawking radiation. Now, let us consider another process of dropping a different book B, instead of A, and see what happens. The subsequent evolution in this case is similar to the case with A, and we will be left with Hawking radiation. However, this final-state Hawking radiation arising from B is (believed by many to be) different from that arising from A in its subtle quantum correlation structure, so that if we have perfect knowledge about the final-state radiation then we can reconstruct what the original book was. This property is called unitarity and is considered to provide the correct picture for black hole dynamics, based on recent theoretical progress. To recap, the information about the original book will not be lost—it will simply be distributed in final-state Hawking radiation in a highly scrambled form.

A puzzling thing occurs, however, if we observe the same phenomenon from the viewpoint of an observer who is falling into the black hole with a book. In this case, the equivalence principle says that the book does not feel gravity (except for the tidal force which is tiny for a large black hole), so it simply passes through the black hole horizon without any disruption. (Recently, this picture was challenged by the so-called firewall argument—the book might hit a collection of higher energy quanta called a firewall, rather than freely fall. Even if so, it does not affect our basic argument below.) This implies that all the information about the book (in fact, the book itself) will be inside the horizon at late times. On the other hand, we have just argued that from a distant observer’s point of view, the information will be outside—first on the horizon and then in Hawking radiation. Which is correct?

One might think that the information is simply duplicated: one copy inside and the other outside. This, however, cannot be the case. Quantum mechanics prohibits faithful copying of full quantum information, the so-called no-cloning theorem. Therefore, it seems that the two pictures by the two observers cannot both be correct.

The proposed solution to this puzzle is interesting—both pictures are correct, but not at the same time. The point is that one cannot be both a distant observer and a falling observer at the same time. If you are a distant observer, the information will be outside, and the interior spacetime must be viewed as non-existent since you can never access it even in principle (because of the existence of the horizon). On the other hand, if you are a falling observer, then you have the interior spacetime in which the information (the book itself) will fall, but this happens only at the cost of losing a part of spacetime in which Hawking radiation lies, which you can never access since you yourself are falling into the black hole. There is no inconsistency in either of these two pictures; only if you artificially “patch” the two pictures, which you cannot physically do, does the apparent inconsistency of information duplication occurs. This somewhat surprising aspect of a system with gravity is called black hole complementarity, pioneered by ‘t Hooft, Susskind, and their collaborators.

What does this discussion of black holes have to do with cosmology, and, in particular the eternally inflating multiverse? In cosmology our space is surrounded by a cosmological horizon. (For example, imagine that space is expanding exponentially; this makes it impossible for us to obtain any signal from regions farther than some distance because objects in these regions recede faster than speed of light. The definition of appropriate horizons in general cases is more subtle, but can be made.) The situation, therefore, is the “inside out” version of the black hole case viewed from a distant observer. As in the case of the black hole, quantum mechanics requires that spacetime on the other side of the horizon—in this case the exterior to the cosmological horizon—must be viewed as non-existent. (In the paper I made this claim based on some simple supportive calculations.) In a more technical term, a quantum state describing the system represents only the region within the horizon—there is no infinite space in any single, consistent description of the system!

If a quantum state represents only space within the horizon, then where is the multiverse, which we thought exists in an eternally inflating space further away from our own horizon? The answer is—probability! The process of creating bubble universes is a probabilistic process in the quantum mechanical sense—it occurs through quantum mechanical tunneling. This implies that, starting from some initially inflating space, we could end up with different universes probabilistically. All different universes—including our own—live in probability space. In a more technical term, a state representing eternally inflating space evolves into a superposition of terms—or branches—representing different universes, but with each of them representing only the region within its own horizon. Note that there is no concept of infinitely large space here, which led to the ill-definedness of probability. The picture of initially large multiverse, naively suggested by general relativity, appears only after “patching” pictures based on different branches together; but this vastly overcounts true degrees of freedom as was the case if we include both the interior spacetime and Hawking radiation in our description of a black hole.

The description of the multiverse presented here provides complete unification of the eternally inflating multiverse and the many worlds interpretation in quantum mechanics. Suppose the multiverse starts from some initial state |\Psi(t_0)\rangle. This state evolves into a superposition of states in which various bubble universes nucleate in various locations. As time passes, a state representing each universe further evolves into a superposition of states representing various possible cosmic histories, including different outcomes of “experiments” performed within that universe. (These “experiments” may, but need not, be scientific experiments—they can be any physical processes.) At late times, the multiverse state |\Psi(t)\rangle will thus contain an enormous number of terms, each of which represents a possible world that may arise from |\Psi(t_0)\rangle consistently with the laws of physics. Probabilities in cosmology and microscopic processes are then both given by quantum mechanical probabilities in the same manner. The multiverse and quantum many worlds are really the same thing—they simply refer to the same phenomenon occurring at (vastly) different scales.

branching

A schematic picture for the evolution of the multiverse state. As t increases, the state evolves into a superposition of states in which various bubble universes nucleate in various locations. Each of these states then evolves further into a superposition of states representing various possible cosmic histories, including different outcomes of experiments performed within that universe.

The picture presented here does not solve all the problems in eternally inflating cosmology. What is the actual quantum state of the multiverse? What is its “initial conditions”? What is time? How does it emerge? The picture, however, does provide a framework to address these further, deep questions, and I have recently made some progress: the basic idea is that the state of the multiverse (which may be selected uniquely by the normalizability condition) never changes, and yet time appears as an emergent concept locally in branches as physical correlations among objects (along the lines of an old idea by DeWitt). Given the length already, I will not elaborate on this new development here. If you are interested, you might want to read my paper.

It is fascinating that physicists can talk about big and deep questions like the ones discussed here based on concrete theoretical progress. Nobody really knows where these explorations will finally lead us to. It seems, however, clear that we live in an exciting era in which our scientific explorations reach beyond what we thought to be the entire physical world, our universe.

Navajo Preparatory High Visit: Reflections by Ana Brown

Evan Miyazono and I recently visited Navajo Preparatory High School in Farmington, New Mexico, the second half of the first exchange of visitors between Caltech and Navajo Prep. Two students and two teachers from the high school visited our campus last summer, spending time touring labs, working on small science and technology projects, and sharing their background and thoughts on science education in the Navajo Nation with us. Evan and I were happy to return the favor and take a trip out to Farmington.

Ana teaching about solar power

We spent the school days giving lectures about light and solar power to the underclassmen and having discussions with the seniors about college applications, college life, and graduate school. We took over physics classes for the entire freshmen class, and spent an hour and a half with each class teaching them the basic E&M they needed to know to understand the wave nature of light and walking them through some simple experiments with lenses and diffraction gratings. When Evan put a piece of paper on which he had cut two very thin slits in front of a green laser-pointer, “oh”s and “ah”s bubbled up from the students as they saw the diffraction pattern appear on the other side of the room. During a math class where Evan was demonstrating how the area and circumference of a circle are related in an intuitive way by breaking up the area of the circle into a rectangle with sides r and pi*r, from where I stood to the side of the classroom, I could hear a student exclaim to his friend “Math is amazing!”.

The next day, after I gave a presentation to the freshmen physics classes on solar power and photovoltaic cells, four students asked for help or resources for their science projects. Two students were making a working model of a “modernized Hogan.” The school has a hogan in the middle of campus where important ceremonies and traditional Navajo gatherings take place. The students want to build a table-top model hogan with working solar water heating and photovoltaic panel to provide warm water and lighting. Another student is working on making a smart phone app for visitors to the Navajo Nation as her senior project. Her app will inform tourists about Navajo landmarks and the significance they hold to the Navajo people. She wants to inform visitors about her culture in an effort to replace the many stereotypes held about native people and Navajos in particular with factual information. These are just a few examples of how students are honoring the traditions of their culture while also taking advantage of new technology and empowering themselves through science education.

Ana speaking to Navajo Prep students

Ana with Navajo Prep Class

I shared with the students stories of friends of mine who had grown up on the Navajo Reservation and the unique issues they confronted in college and afterward. Students who come from tribal reservations often experience homesickness to a much greater degree than other groups when they go away to college. Many of these young adults are accustomed to a very tight community and strong sense of belonging and support that they feel in their hometown, so leaving that community to join a huge group of strangers with cultures foreign from their own can be a big challenge. I gave an informal seminar to the senior class where I discussed college in general as well as issues specific to native students. I gave them advice gleaned from my own experiences as well as the experiences of some of my Navajo friends. Evan and I also answered tons of questions that the students had about all aspects of college—getting in, financial aid, being successful, and finding balance. They asked how to approach a professor about doing research in their lab and how to budget their finances, what kind of summer job they should look for, and how to balance family life and ties with college life. The seniors had so many questions that together we spent more than two hours discussing these topics and answering general and specific questions. I was really happy we could provide so much useful and desired information for these young scholars.

In our free time Evan and I got to spend more time with teachers and students, sharing meals, information, and ideas. It was great to get to know the students and teachers better and learn more about their perspectives and experiences, and how education is fitting into their lives. I look forward to continuing to develop these relationships from afar. We already have plans to mentor a couple of students with their science and senior projects and hope to recruit more Caltech grad students to serve as mentors. Supporting and encouraging these native students in their participation in math and science fields, and higher education in general, as well as helping them to maintain a strong commitment and connection to their culture and families is something that I want to continue to foster as a mentor and ally of the school. I want to thank IQIM for providing the funding for this trip that made these connections possible.

A Quantum Adventure

by Jorge Cham

How do you make something that has never existed before?

I often get suggestions for comics I should draw, which I welcome because A) I like to think of PHD Comics as a global collaborative effort and B) after 17 years, I’m almost out of ideas. This particular suggestion came from Chen-Lung Hung, a postdoc in Physics at Caltech:

PANEL 1 – Ask a scientist: “What motivates you to do the research you do?”

PANEL 2 – What people expect them to answer: “This can lead to real-life applications such as A, B, C, D, etc.”

PANEL 3 – How a real scientist would answer: “Because it’s cool.”

blog_02s

Ok, granted, the punchline needs work. Chen-Lung also asked me to make it clear that his research has important real-life applications, should someone from NSF, who funds his work, happen to be reading this blog.

Chen-Lung’s work with Prof. Jeff Kimble of Caltech’s IQIM is the subject of the third installment in our animated series of explanations of Quantum concepts and devices.

“The problem with atoms,” Prof. Kimble said at one point during our 3-4 hour conversation, “is that they exist in three dimensional space.” I didn’t know that was a problem (unless you expect them to exist in more than 3 dimensions), but Jeff explained that it means it’s very hard to control Quantum systems because the world is wide open, and information can leak and be corrupted from any direction. After a entire academic career making breakthroughs with one type of Quantum System, he’s now directing his group towards a new, experimental type which they believe has more potential for building devices with many Quantum Objects. As Jeff says in the video, “It’s a privilege to be able to explore.”

blog_04s

Shaping light, trapping atoms, alligator waveguides… The goal, Jeff and Chen-lung explained, is to make systems that are “surprising.” Not surprisingly, it was really hard to draw this video. How do you depict something that has never existed before? And more importantly, do you draw alligators differently from crocodiles? (Did you know alligators only exist in two places in the world: the Southern part of the United States, and in China?).

blog_03s

Hopefully, those of you watching will get some understanding of some key Quantum concepts and what it takes to build and manipulate Quantum systems, but to be honest, I make these videos because I think the work is really cool.

Jeff and Chen-Lung: thanks for taking us along on this adventure of yours, the privilege is all ours.

Watch the third installment of this series:

Jorge Cham is the creator of Piled Higher and Deeper (www.phdcomics.com).

CREDITS:

Featuring: Jeff Kimble and Chen-Lung Hung
Animated by Jorge Cham

Produced in Partnership with the Institute for Quantum Information and Matter (http://iqim.caltech.edu) at Caltech with funding provided by the National Science Foundation and the Betty and Gordon Moore Foundation.