Wouldn’t you like to know what’s going on in my mind?

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I suppose most theoretical physicists who (like me) are comfortably past the age of 60 worry about their susceptibility to “crazy-old-guy syndrome.” (Sorry for the sexism, but all the victims of this malady I know are guys.) It can be sad when a formerly great scientist falls far out of the mainstream and seems to be spouting nonsense.

Matthew Fisher is only 55, but reluctance to be seen as a crazy old guy might partially explain why he has kept pretty quiet about his passionate pursuit of neuroscience over the past three years. That changed two months ago when he posted a paper on the arXiv about Quantum Cognition.

Neuroscience has a very seductive pull, because it is at once very accessible and very inaccessible. While a theoretical physicist might think and write about a brane even without having or seeing a brane, everybody’s got a brain (some scarecrows excepted). On the other hand, while it’s not too hard to write down and study the equations that describe a brane, it is not at all easy to write down the equations for a brain, let alone solve them. The brain is fascinating because we know so little about it. And … how can anyone with a healthy appreciation for Gödel’s Theorem not be intrigued by the very idea of a brain that thinks about itself?

(Almost) everybody's got a brain.

(Almost) everybody’s got a brain.

The idea that quantum effects could have an important role in brain function is not new, but is routinely dismissed as wildly implausible. Matthew Fisher begs to differ. And those who read his paper (as I hope many will) are bound to conclude: This old guy’s not so crazy. He may be onto something. At least he’s raising some very interesting questions.

My appreciation for Matthew and his paper was heightened further this Wednesday, when Matthew stopped by Caltech for a lunch-time seminar and one of my interminable dinner-time group meetings. I don’t know whether my brain is performing quantum information processing (and neither does Matthew), but just the thought that it might be is lighting me up like a zebrafish.

Following Matthew, let’s take a deep breath and ask ourselves: What would need to be true for quantum information processing to be important in the brain? Presumably we would need ways to (1) store quantum information for a long time, (2) transport quantum information, (3) create entanglement, and (4) have entanglement influence the firing of neurons. After a three-year quest, Matthew has interesting things to say about all of these issues. For details, you should read the paper.

Matthew argues that the only plausible repositories for quantum information in the brain are the Phosphorus-31 nuclear spins in phosphate ions. Because these nuclei are spin-1/2, they have no electric quadrupole moments and hence corresponding long coherence times — of order a second. That may not be long enough, but phosphate ions can be bound with calcium ions into objects called Posner clusters, each containing six P-31 nuclei. The phosphorus nuclei in Posner clusters might have coherence times greatly enhanced by motional narrowing, perhaps as long as weeks or even longer.

Where energy is being consumed in a cell, ATP sometimes releases diphosphate ions (what biochemists call pyrophosphate), which are later broken into two separate phosphate ions, each with a single P-31 qubit. Matthew argues that the breakup of the diphosphate, catalyzed by a suitable enzyme, will occur at an enhanced rate when these two P-31 qubits are in a spin singlet rather than a spin triplet. The reason is that the enzyme has to grab ahold of the diphosphate molecule and stop its rotation in order to break it apart, which is much easier when the molecule has even rather than odd orbital angular momentum; therefore due to Fermi statistics the spin state of the P-31 nuclei must be antisymmetric. Thus wherever ATP is consumed there is a plentiful source of entangled qubit pairs.

If the phosphate molecules remain unbound, this entanglement will decay in about a second, but it is a different story if the phosphate ions group together quickly enough into Posner clusters, allowing the entanglement to survive for a much longer time. If the two members of an entangled qubit pair are snatched up by different Posner clusters, the clusters may then be transported into different cells, distributing the entanglement over relatively long distances.

(a) Two entangled Posner clusters. Each dot is a P-31 nuclear spin, and each dashed line represents a singlet pair. (b) Many entangled Posner clusters. [From the paper]

(a) Two entangled Posner clusters. Each dot is a P-31 nuclear spin, and each dashed line represents a singlet pair. (b) Many entangled Posner clusters. [From Fisher 2015]

What causes a neuron to fire is a complicated story that I won’t attempt to wade into. Suffice it to say that part of the story may involve the chemical binding of a pair of Posner clusters which then melt if the environment is sufficiently acidic, releasing calcium ions and phosphate ions which enhance the firing. The melting rate depends on the spin state of the six P-31 nuclei within the cluster, so that entanglement between clusters in different cells may induce nonlocal correlations among different neurons, which could be quite complex if entanglement is widely distributed.

This scenario raises more questions than it answers, but these are definitely scientific questions inviting further investigation and experimental exploration. One thing that is far from clear at this stage is whether such quantum correlations among neurons (if they exist at all) would be easy to simulate with a classical computer. Even if that turns out to be so, these potential quantum effects involving many neurons could be fabulously interesting. IQIM’s mission is to reach for transformative quantum science, particularly approaches that take advantage of synergies between different fields of study. This topic certainly qualifies.* It’s going to be great fun to see where it leads.

If you are a young and ambitious scientist, you may be contemplating the dilemma: Should I pursue quantum physics or neuroscience? Maybe, just maybe, the right answer is: Both.

*Matthew is the only member of the IQIM faculty who is not a Caltech professor, though he once was.

Surprise Happens in Experiments

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The discovery of high temperature superconductivity in copper-oxide-based ceramics (cuprates) in 1986 created tremendous excitement in the scientific community. For the first time superconductivity, the ability of a material to conduct electricity with zero energy loss to heat, was possible at temperatures an order of magnitude higher than what were previously thought possible. Thus began the dream of room temperature superconductivity, a dream that has been heavily sought but still unfulfilled to this day.

The difficulty in creating a room temperature superconductor is that we still do not even understand how cuprate high temperature superconductors exactly work. We have known that the superconductivity is born from removing or adding a proper amount of electrons to an insulating antiferromagnet. What is more is that the material experiences a mysterious region, usually called pseudogap, when transiting from the insulating antiferromagnet into the superconductor. For decades, scientists have debated whether the pseudogap in cuprates is a continuous evolution into superconductivity or a competing phase of matter with distinct symmetry properties, and some believe that a better understanding of its nature and relationship to superconductivity can help to pave a path towards room temperature superconductivity.

The compound that we are studying, strontium-iridium-oxide (Sr2IrO4), is a promising candidate for a new family of high temperature superconductors. Recent experimental findings in Sr2IrO4 reveal great similarities between Sr2IrO4 and cuprates. Sr2IrO4 is a novel insulator at room temperature and turns into an antiferromagnet below a critical temperature called Néel temperature (TN). With a certain amount of electrons added or removed by introducing foreign atoms in it, Sr2IrO4 enters into the pseudogap regime. At an even higher charge carrier concentration and a lower temperature, Sr2IrO4 exhibits strong signatures of unconventional superconductivity. A summary of the evolution of Sr2IrO4 as functions of charge carrier density and temperature, usually referred as a phase diagram, is depicted into a cartoon below, which mimics that of cuprates.

A cartoon showing similarities between Sr2IrO4 and Cuprates

A cartoon showing similarities between Sr2IrO4 and cuprates.

Our experimental results on the multipolar order in Sr2IrO4 further bridges the connection between Sr2IrO4 and cuprates. On one hand, there have been growing experimental evidences in recent years to support the presence of symmetry breaking phases of matter in the pseudogap regime of cuprates. On the other hand, the discovery of multipolar order in Sr2IrO4 where the psuedogap phenomenon has also been observed suggests a possible connection between these two. To establish the relationship between the multipolar order and the pseudogap in Sr2IrO4, one needs to compare the temperature scales at which each of them happens. So far, we have bounded a line in the Sr2IrO4 phase diagram for the multipolar ordered phase that breaks the 90o rotational symmetry from its high temperature state. However, the onset temperature for the pseudogap in Sr2IrO4 remains unknown in the community.

An artistic rendition of rotational anisotropy patterns both above and below the transition temperature T_Ω where the multipolar order happens, showing the 90^o rotational symmetry breaking across T_Ω

An artistic rendition of rotational anisotropy patterns both above and below the transition temperature T_Ω where the multipolar order happens, showing the 90^o rotational symmetry breaking across T_Ω.

Retrospectively, the scientific story was told as above in which it seems our experiment perfectly fits in a void in the connections between Sr2IrO4 and cuprates. In reality, this experiment is my first encounter of serendipity in scientific researches. When we started our experiment, there were no experimental indications about pseudogap or superconductivity in Sr2IrO4, and we were just planning to refine its antiferromagnetic structure based upon its recently refined crystallographic structure. This joyful surprise makes me aware of the importance of sensitivity to unexpected results, especially in a developing field. Another surprise to me is the technique that we used in this study, namely rotational anisotropy optical second harmonic generation. This technique is as simple as shining light of frequency ω at the sample from a series of angles and collecting light of frequency 2ω reflected from the sample. The novelty of our setup is to move the light around the sample as opposed to the other way in the traditional version of this technique. Exactly thank to this seemingly trivial novelty, we are able to probe the multipolar order that is still challenging for other more sophisticated symmetry sensitive techniques. To me, it is this experience that is more valuable, and that is what I feel happiest to share.

Although the dream of room temperature superconductivity is still unfulfilled, the cross comparisons between Sr2IrO4 and cuprates could be insightful in determining the important factors for superconductivity, and eventually make the journey towards the dream.

Please find more details in our paper and Caltech media.

Artist's rendition of spatially segregated domains of multipolar order in the Sr2IrO4 crystal.

Artist’s rendition of spatially segregated domains of multipolar order in the Sr2IrO4 crystal.

Explaining Quantum Physics to Newton… in 140 characters

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Sir Isaac Newton is considered by many as the greatest physicist of all time. But despite Newton’s contributions to classical physics, the man never even fathomed that the world was actually governed by the equations of quantum mechanics. We think it is time to right that wrong. With your help, we plan to send a Tweet back in time (something about time machines restricts quantum telegraphs to 140 characters) that explains what quantum is all about to Sir Isaac. This mini competition is taking place on our Twitter account over @IQIM_Caltech and ends on November 5th, 2015. The prize is a one-year digital subscription to Scientific American.

For more details, please see below. This mini competition is part of Quantum Shorts, a flash fiction competition conceived and executed by our friends at the Center for Quantum Technologies.

QSmini_oct28_twitter

Let the games begin!

Nothing has been done yet. The world is your oyster…still.

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The three things that come to mind when I watch Simon’s video are: travel, perspective and discomfort. They remind me of some of the things I also said in my TEDx talk titled “Get Uncomfortable Now”.

Simon’s video exemplifies a lot of what I feel is true in filmmaking as well. He goes running to clear his mind and get more creative, I take long walks when I’m stuck at a point in my screenplays or edits. He travels to learn more about what’s out there, I travel to absorb culture as well, he tries diversity of experiences to enrich his mind, so do I in a selfish desire to enrich every character I write or direct; all with the ultimate goal of growth & transience: emotional, physical, mental.

Simon also says something very exciting in the film, “there’s so much left to do out there”, a thought that isn’t expressed that often, the idea that “I can do something novel right here in the lab” makes the chance of innovation, success and achievement very tangible; achievable. That honesty, excitement and drive is important to be repeated in an otherwise very jaded and intimidated world. The belief in the power of the individual driving forward and having the potential to change the status quo, in the lab and outside, is critical.

It was hard to get Simon to narrow it down to the one hobby that drove him. After Debaleena’s video being internal and about family, we knew we wanted something more external. Filming in Griffith park is usually a nightmare but that early morning, we got everything we wanted minus possibly a clearer view of downtown LA, thanks to Marcia Brown’s usual detailed planning.

The shoot was complete with a steadicam operator, running videos and even the spotting of a snake!

The most memorable thing for me are Simon’s slow motion shots that highlight the sound of foot steps, of pushing forward, step by step, one ahead of the other; that basic contact that lunges us into the future. There was something very “grounding” about watching that, no pun intended.

Without further ado, here’s the video:

“Experimenting” with women-in-STEM stereotypes

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When signing up for physics grad school, I didn’t expect to be interviewed by a comedienne on a spoof science show about women in STEM.

Last May, I received an email entitled “Amy Poehler’s Smart Girls.” The actress, I read, had co-founded the Smart Girls organization to promote confidence and creativity in preteens and teens. Smart Girls was creating a webseries hosted by Megan Amram, author of Science…for Her! The book parodies women’s magazines and ridicules stereotypes of women as unsuited for science.

Megan would host the webseries, “Experimenting with Megan,” in character as an airhead. She planned to interview “kick-ass lady scientists/professors/doctors” in a parody of a talk show. Would I, the email asked, participate?

I’m such a straitlaced fogey, I never say “kick-ass.” I’m such a workaholic, I don’t watch webshows. I’ve not seen Parks and Recreation, the TV series that starred Amy Poehler and for which Megan wrote. The Hollywood bug hasn’t bitten me, though I live 30 minutes from Studio City.

But I found myself in a studio the next month. Young men and women typed on laptops and chattered in the airy, bright waiting lounge. Beyond a doorway lay the set, enclosed by fabric-covered walls that prevented sounds from echoing. Script-filled binders passed from hand to hand, while makeup artists, cameramen, and gophers scurried about.

APSG-Nicole-Yunger-Halpern1

Being interviewed on “Experimenting with Megan.”

Disney’s Mouseketeers couldn’t have exuded more enthusiasm or friendliness than the “Experimenting” team. “Can I bring you a bottle of water?” team members kept asking me and each other. “Would you like a chair?” The other women who interviewed that day—two biologist postdocs—welcomed me into their powwow. Each of us, we learned, is outnumbered by men at work. None of us wears a lab coat, despite stereotypes of scientists as white-coated. Each pours herself into her work: One postdoc was editing a grant proposal while off-set.

I watched one interview, in which Megan asked why biologists study fruit flies instead of “cuter” test subjects. Then I stepped on-set beside her. I perched on an armchair that threatened to swallow my 5’ 3.5” self.* Textbooks, chemistry flasks, and high-heeled pumps stood on the bookshelves behind Megan.

The room quieted. A clapperboard clapped: “Take one.” Megan thanked me for coming, then launched into questions.

Megan hadn’t warned me what she’d ask. We began with “Do you like me?” and “What is the ‘information’ [in ‘quantum information theory’], and do you ever say, ‘Too much information’?” Each question rode hot on the heels of the last. The barrage reminded me of interviews for not-necessarily-scientific scholarships. Advice offered by one scholarship-committee member, the year before I came to Caltech, came to mind: Let loose. Act like an athlete tearing down the field, the opposing team’s colors at the edges of your vision. Savor the challenge.

I savored it. I’d received instructions to play the straight man, answering Megan’s absurdity with science. To “Too much information?” I parried that we can never know enough. When I mentioned that quantum mechanics describes electrons, Megan asked about the electricity she feels upon seeing Chris Hemsworth. (I hadn’t heard of Chris Hemsworth. After watching the interview online, a friend reported that she’d enjoyed the reference to Thor. “What reference to Thor?” I asked. Hemsworth, she informed me, plays the title character.) I dodged Chris Hemsworth; caught “electricity”; and stretched to superconductors, quantum devices whose charges can flow forever.

Academic seminars conclude with question-and-answer sessions. If only those Q&As zinged with as much freshness and flexibility as Megan’s.

The “Experimenting” approach to stereotype-blasting diverges from mine. High-heeled pumps, I mentioned, decorated the set. The “Experimenting” team was parodying the stereotype of women as shoe-crazed. “Look at this stereotype!” the set shouts. “Isn’t it ridiculous?”

As a woman who detests high heels and shoe shopping, I prefer to starve the stereotype of justification. I’ve preferred reading to shopping since before middle school, when classmates began frequenting malls. I feel more comfortable demonstrating, through silence, how little shoes interest me. I’d rather offer no reason for anyone to associate me with shoes.**

I scarcely believe that I appear just after a “sexy science” tagline and a hot-or-not quiz. Before my interview on her quantum episode, Megan discussed the relationship between atoms and Adams. Three guests helped her, three Hollywood personalities named “Adam.”*** Megan held up cartoons of atoms, and photos of Adams, and asked her guests to rate their hotness. I couldn’t have played Megan’s role, couldn’t imagine myself in her (high-heeled) shoes.

But I respect the “Experimenting” style. Megan’s character serves as a foil for the interviewee I watched. Megan’s ridiculousness underscored the postdoc’s professionalism and expertise.

According to online enthusiasm, “Experimenting” humor resonates with many viewers. So diverse is the community that needs introducing to STEM, diverse senses of humor have roles to play. So deep run STEM’s social challenges, multiple angles need attacking.

Just as diverse perspectives can benefit women-in-STEM efforts, so can diverse perspectives benefit STEM. Which is why STEM needs women, Adams, shoe-lovers, shoe-haters…and experimentation.

With gratitude to the “Experimenting” team for the opportunity to contribute to its cause. The live-action interview appears here (beginning at 2:42), and a follow-up personality quiz appears here.

*If you’re 5′ 3.5″, every half-inch matters.

**Except when I blog about how little I wish to associate with shoes.

***Megan introduced her guests as “Adam Shankman, Adam Pally, and an intern that we made legally change his name to Adam to be on the show.” The “intern” is Adam Rymer, president of Legendary Digital Networks. Legendary owns Amy Poehler’s Smart Girls.

Quantum Shorts 2015: A “flash fiction” competition

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A blog on everything quantum is the perfect place to announce the launch of the 2015 Quantum Shorts competition. The contest encourages readers to create quantum-themed “flash fiction”: a short story of no more than 1000 words that is inspired by quantum physics. Scientific American, the longest continuously published magazine in the U.S., Nature, the world’s leading multidisciplinary science journal, and Tor Books, the leading science fiction and fantasy publisher, are media partners for the contest run by the Centre for Quantum Technologies at the National University of Singapore. Entries can be submitted now through 11:59:59 PM ET on December 1, 2015 at http://shorts.quantumlah.org.

“Quantum physics seems to inspire creative minds, so we can’t wait to see what this year’s contest will bring,” says Scientific American Editor in Chief and competition judge Mariette DiChristina.

A panel of judges will select the winners and runner-ups in two categories: Open and Youth. The public will also vote and decide the People’s Choice Prize from entries shortlisted across both categories. Winners will receive a trophy, a cash prize and a one-year digital subscription to ScientificAmerican.com. The winner of the Open category will also be featured on ScientificAmerican.com.

QS2015_bannerThe quantum world offers lots of scope for enthralling characters and mind-blowing plot twists, according to Artur Ekert, director of the Centre for Quantum Technologies and co-inventor of quantum cryptography. “A writer has plenty to play with when science allows things to be in two places – or even two universes – at once,” he says. “The result might be funny, tense or even confusing. But it certainly won’t be boring.” Artur is one of the Open category judges.

Another judge is Colin Sullivan, editor of Futures, Nature’s own science-themed fiction strand. “Science fiction is a powerful and innovative genre,” Colin says. “We are excited to see what kinds of stories quantum physics can inspire.”

The 2015 Quantum Shorts contest is also supported by scientific partners around the world. The Institute for Quantum Information and Matter is proud to sponsor this competition, along with our friends at the Centre for Engineered Quantum Systems, an Australian Research Council Centre of Excellence, the Institute for Quantum Computing at the University of Waterloo, and the Joint Quantum Institute, a research partnership between the University of Maryland and the National Institute of Standards and Technology.

Submissions to Quantum Shorts 2015 are limited to 1000 words and can be entered into the Quantum Shorts competition via the website at http://shorts.quantumlah.org, which also features a full set of rules and guidelines.

For more information about the organizer and partners, please visit the competition website at http://shorts.quantumlah.org.

Toward physical realizations of thermodynamic resource theories

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“This is your arch-nemesis.”

The thank-you slide of my presentation remained onscreen, and the question-and-answer session had begun. I was presenting a seminar about thermodynamic resource theories (TRTs), models developed by quantum-information theorists for small-scale exchanges of heat and work. The audience consisted of condensed-matter physicists who studied graphene and photonic crystals. I was beginning to regret my topic’s abstractness.

The question-asker pointed at a listener.

“This is an experimentalist,” he continued, “your arch-nemesis. What implications does your theory have for his lab? Does it have any? Why should he care?”

I could have answered better. I apologized that quantum-information theorists, reared on the rarefied air of Dirac bras and kets, had developed TRTs. I recalled the baby steps with which science sometimes migrates from theory to experiment. I could have advocated for bounding, with idealizations, efficiencies achievable in labs. I should have invoked the connections being developed with fluctuation results, statistical mechanical theorems that have withstood experimental tests.

The crowd looked unconvinced, but I scored one point: The experimentalist was not my arch-nemesis.

“My new friend,” I corrected the questioner.

His question has burned in my mind for two years. Experiments have inspired, but not guided, TRTs. TRTs have yet to drive experiments. Can we strengthen the connection between TRTs and the natural world? If so, what tools must resource theorists develop to predict outcomes of experiments? If not, are resource theorists doing physics?

http://everystevejobsvideo.com/steve-jobs-qa-session-excerpt-following-antennagate-2010/

A Q&A more successful than mine.

I explore answers to these questions in a paper released today. Ian Durham and Dean Rickles were kind enough to request a contribution for a book of conference proceedings. The conference, “Information and Interaction: Eddington, Wheeler, and the Limits of Knowledge” took place at the University of Cambridge (including a graveyard thereof), thanks to FQXi (the Foundational Questions Institute).

What, I asked my advisor, does one write for conference proceedings?

“Proceedings are a great opportunity to get something off your chest,” John said.

That seminar Q&A had sat on my chest, like a pet cat who half-smothers you while you’re sleeping, for two years. Theorists often justify TRTs with experiments.* Experimentalists, an argument goes, are probing limits of physics. Conventional statistical mechanics describe these regimes poorly. To understand these experiments, and to apply them to technologies, we must explore TRTs.

Does that argument not merit testing? If experimentalists observe the extremes predicted with TRTs, then the justifications for, and the timeliness of, TRT research will grow.

http://maryqin.com/wp-content/uploads/2014/05/

Something to get off your chest. Like the contents of a conference-proceedings paper, according to my advisor.

You’ve read the paper’s introduction, the first eight paragraphs of this blog post. (Who wouldn’t want to begin a paper with a mortifying anecdote?) Later in the paper, I introduce TRTs and their role in one-shot statistical mechanics, the analysis of work, heat, and entropies on small scales. I discuss whether TRTs can be realized and whether physicists should care. I identify eleven opportunities for shifting TRTs toward experiments. Three opportunities concern what merits realizing and how, in principle, we can realize it. Six adjustments to TRTs could improve TRTs’ realism. Two more-out-there opportunities, though less critical to realizations, could diversify the platforms with which we might realize TRTs.

One opportunity is the physical realization of thermal embezzlement. TRTs, like thermodynamic laws, dictate how systems can and cannot evolve. Suppose that a state R cannot transform into a state S: R \not\mapsto S. An ancilla C, called a catalyst, might facilitate the transformation: R + C \mapsto S + C. Catalysts act like engines used to extract work from a pair of heat baths.

Engines degrade, so a realistic transformation might yield S + \tilde{C}, wherein \tilde{C} resembles C. For certain definitions of “resembles,”** TRTs imply, one can extract arbitrary amounts of work by negligibly degrading C. Detecting the degradation—the work extraction’s cost—is difficult. Extracting arbitrary amounts of work at a difficult-to-detect cost contradicts the spirit of thermodynamic law.

The spirit, not the letter. Embezzlement seems physically realizable, in principle. Detecting embezzlement could push experimentalists’ abilities to distinguish between close-together states C and \tilde{C}. I hope that that challenge, and the chance to violate the spirit of thermodynamic law, attracts researchers. Alternatively, theorists could redefine “resembles” so that C doesn’t rub the law the wrong way.

http://www.eoht.info/page/Laws+of+thermodynamics+(game+version)

The paper’s broadness evokes a caveat of Arthur Eddington’s. In 1927, Eddington presented Gifford Lectures entitled The Nature of the Physical World. Being a physicist, he admitted, “I have much to fear from the expert philosophical critic.” Specializing in TRTs, I have much to fear from the expert experimental critic. The paper is intended to point out, and to initiate responses to, the lack of physical realizations of TRTs. Some concerns are practical; some, philosophical. I expect and hope that the discussion will continue…preferably with more cooperation and charity than during that Q&A.

If you want to continue the discussion, drop me a line.

*So do theorists-in-training. I have.

**A definition that involves the trace distance.

Bits, Bears, and Beyond in Banff: Part Deux

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You might remember that about one month ago, Nicole blogged about the conference Beyond i.i.d. in information theory and told us about bits, bears, and beyond in Banff. I was very pleased that Nicole did so, because this conference has become one of my favorites in recent years (ok, it’s my favorite). You can look at her post to see what is meant by “Beyond i.i.d.” The focus of the conference includes cutting-edge topics in quantum Shannon theory, and the conference still has a nice “small world” feel to it (for example, the most recent edition and the first one featured a music session from participants). Here is a picture of some of us having a fun time:

Will Matthews, Felix Leditzky, me, and Nilanjana Datta (facing away) singing

Will Matthews, Felix Leditzky, me, and Nilanjana Datta (facing away) singing “Jamaica Farewell”.

The Beyond i.i.d. series has shaped a lot of the research going on in this area and has certainly affected my own research directions. The first Beyond i.i.d. was held in Cambridge, UK in January 2013, organized by Nilanjana Datta and Renato Renner. It had a clever logo, featuring cyclists of various sorts biking one after another, the first few looking the same and the ones behind them breaking out of the i.i.d. pattern:

Screen Shot 2015-09-12 at 3.55.17 PM

It was also at the Cambridge edition that the famous entropy zoo first appeared, which has now been significantly updated, based on recent progress in the area. The next Beyond i.i.d. happened in Singapore in May 2014, organized by Marco Tomamichel, Vincent Tan, and Stephanie Wehner. (Stephanie was a recent “quantum woman” for her work on a loophole-free Bell experiment.)

The tradition continued this past summer in beautiful Banff, Canada. I hope that it goes on for a long time. At least I have next year’s to look forward to, which will be in beachy Barcelona in the summertime, (as of now) planned to be just one week before Alexander Holevo presents the Shannon lecture in Barcelona at the ISIT 2016 conference (by the way, this is the first time that a quantum information theorist has won the prestigious Shannon award).

So why am I blabbing on and on about the Beyond i.i.d. conference if Nicole already wrote a great summary of the Banff edition this past summer? Well, she didn’t have room in her blog post to cover one of my favorite topics that was discussed at my favorite conference, so she graciously invited me to discuss it here.

The driving question of my new favorite topic is “What is the right notion of a quantum Markov chain?” The past year or so has seen some remarkable progress in this direction. To motivate it, let’s go back to bears, and specifically bear attacks (as featured in Nicole’s post). In Banff, the locals there told us that they had never heard of a bear attacking a group of four or more people who hike together. But let’s suppose that Alice, Bob, and Eve ignore this advice and head out together for a hike in the mountains. Also, in a different group are 50 of Alice’s sisters, but the park rangers are focusing their binoculars on the group of three (Alice, Bob, and Eve), observing their movements, because they are concerned that a group of three will run into trouble.

In the distance, there is a clever bear observing the movements of Alice, Bob, and Eve, and he notices some curious things. If he looks at Alice and Bob’s movements alone, they appear to take each step randomly, but for the most part together. That is, their steps appear correlated. He records their movements for some time and estimates a probability distribution p(a,b) that characterizes their movements. However, if he considers the movements of Alice, Bob, and Eve all together, he realizes that Alice and Bob are really taking their steps based on what Eve does, who in turn is taking her steps completely at random. So at this point the bear surmises that Eve is the mediator of the correlations observed between Alice and Bob’s movements, and when he writes down an estimate for the probability distribution p(a,b,e) characterizing all three of their movements, he notices that it factors as p(a,b,e) = p(a|e) p(b|e) p(e). That is, the bear sees that the distribution forms a Markov chain.

“What is an important property of such a Markov chain?“, asks the bear. Well, neglecting Alice’s movements (summing over the a variable), the probability distribution reduces to p(b|e) p(e), because p(a|e) is a conditional probability distribution. A characteristic of a Markov probability distribution is that one could reproduce the original distribution p(a,b,e) simply by acting on the e variable of p(b|e) p(e) with the conditional probability distribution p(a|e). So the bear realizes that it would be possible for Alice to be lost and subsequently replaced by Eve calling in one of Alice’s sisters, such that nobody else would notice anything different from before — it would appear as if the movements of all three were unchanged once this replacement occurs. Salivating at his realization, the bear takes Eve briefly aside without any of the others noticing. The bear explains that he will not eat Eve and will instead eat Alice if Eve can call in one of Alice’s sisters and direct her movements to be chosen according to the distribution p(a|e). Eve, realizing that her options are limited (ok, ok, maybe there are other options…), makes a deal with the bear. So the bear promptly eats Alice, and Eve draws in one of Alice’s sisters, whom Eve then directs to walk according to the distribution p(a|e). This process repeats, going on and on, and all the while, the park rangers, focusing exclusively on the movements on the party of three, don’t think anything of what’s going because they observe that the joint distribution p(a,b,e) describing the movements of “Alice,” Bob, and Eve never seems to change (let’s assume that the actions of the bear and Eve are very fast 🙂 ). So the bear is very satisfied after eating Alice and some of her sisters, and Eve is pleased not to be eaten, at the same time never having cared too much for Alice or any of her sisters.

A natural question arises: “What could Alice and Bob do to prevent this terrible situation from arising, in which Alice and so many of her sisters get eaten without the park rangers noticing anything?” Well, Alice and Bob could attempt to coordinate their movements independently of Eve’s. Even better, before heading out on a hike, they could make sure to have brought along several entangled pairs of particles (and perhaps some bear spray). If Alice and Bob choose their movements according to the outcomes of measurements of the entangled pairs, then it would be impossible for Alice to be eaten and the park rangers not to notice. That is, the distribution describing their movements could never be described by a Markov chain distribution of the form p(a|e) p(b|e) p(e). Thus, in such a scenario, as soon as the bear attacks Alice and then Eve replaces her with one of her sisters, the park rangers would immediately notice something different about the movements of the party of three and then figure out what is going on. So at least Alice could save her sisters…

What is the lesson here? A similar scenario is faced in quantum key distribution. Eve and other attackers (such as a bear) might try to steal what is there in Alice’s system and then replace it with something else, in an attempt to go undetected. If the situation is described by classical physics, this would be possible if Eve had access to a “hidden variable” that dictates the actions of Alice and Bob. But according to Bell’s theorem or the monogamy of entanglement, it is impossible for a “hidden variable” strategy to mimic the outcomes of measurements performed on sufficiently entangled particles.

Since we never have perfectly entangled particles or ones whose distributions exactly factor as Markov chains, it would be ideal to quantify, for a given three-party quantum state of Alice, Bob, and Eve, how well one could recover from the loss of the Alice system by Eve performing a recovery channel on her system alone. This would help us to better understand approximate cases that we expect to appear in realistic scenarios. At the same time, we could have a more clear understanding of what constitutes an approximate quantum Markov chain.

Now due to recent results of Fawzi and Renner, we know that this quantification of quantum non-Markovianity is possible by using the conditional quantum mutual information (CQMI), a fundamental measure of information in quantum information theory. We already knew that the CQMI is non-negative when evaluated for any three-party quantum state, due to the strong subadditivity inequality, but now we can say more than that: If the CQMI is small, then Eve can recover well from the loss of Alice, implying that the reduced state of Alice and Bob’s system could not have been too entangled in the first place. Relatedly, if Eve cannot recover well from the loss of Alice, then the CQMI cannot be small. The CQMI is the quantity underlying the squashed entanglement measure, which in turn plays a fundamental role in characterizing the performance of realistic quantum key distribution systems.

Since the original results of Fawzi and Renner appeared on the arXiv, this topic has seen much activity in “quantum information land.” Here are some papers related to this topic, which have appeared in the past year or so (apologies if I missed your paper!):

Renyi generalizations of the conditional quantum mutual information
Fidelity of recovery, geometric squashed entanglement, and measurement recoverability
Renyi squashed entanglement, discord, and relative entropy differences
Squashed entanglement, k-extendibility, quantum Markov chains, and recovery maps
Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution
Multipartite quantum correlations and local recoverability
Monotonicity of quantum relative entropy and recoverability
Quantum Markov chains, sufficiency of quantum channels, and Renyi information measures
The Fidelity of Recovery is Multiplicative
Universal recovery map for approximate Markov chains
Recoverability in quantum information theory
Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
Universal recovery from a decrease of quantum relative entropy

Some of the papers are admittedly that of myself and my collaborators, but hey!, please forgive me, I’ve been excited about the topic. We now know simpler proofs of the original Fawzi–Renner results and extensions of them that apply to the quantum relative entropy as well. Since the quantum relative entropy is such a fundamental quantity in quantum information theory, some of the above papers provide sweeping ramifications for many foundational statements in quantum information theory, including entanglement theory, quantum distinguishability, the Holevo bound, quantum discord, multipartite information measures, etc. Beyond i.i.d. had a day of talks dedicated to the topic, and I think we will continue seeing further developments in this area.

The enigma of Robert Hooke

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In 1675, Robert Hooke published the “true mathematical and mechanical form” for the shape of an ideal arch.  However, Hooke wrote the theory as an anagram,

abcccddeeeeefggiiiiiiiillmmmmnnnnnooprrsssttttttuuuuuuuux.

Its solution was never published in his lifetime.  What was the secret hiding in these series of letters?

Hooke-Arch

An excerpt from Hooke’s manuscript “A description of helioscopes, and some other instruments”.

The arch is one of the fundamental building blocks in architecture.  Used in bridges, cathedrals, doorways, etc., arches provide an aesthetic quality to the structures they dwell within.  Their key utility comes from their ability to support weight above an empty space, by distributing the load onto the abutments at its feet.  A dome functions much like an arch, except a dome takes on a three-dimensional shape whereas an arch is two-dimensional.  Paradoxically, while being the backbone of the many edifices, arches and domes themselves are extremely delicate: a single misplaced component along its curve, or an improper shape in the design would spell doom for the entire structure.

The Romans employed the rounded arch/dome—in the shape of a semicircle/hemisphere–in their bridges and pantheons.  The Gothic architecture favored the pointed arch and the ribbed vault in their designs.  However, neither of these arch forms were adequate for the progressively grander structures and more ambitious cathedrals sought in the 17th century.  Following the great fire of London in 1666, a massive rebuilding effort was under way.  Among the new public buildings, the most prominent was to be St. Paul’s Cathedral with its signature dome.  A modern theory of arches was sorely needed: what is the perfect shape for an arch/dome?

Christopher Wren, the chief architect of St. Paul’s Cathedral, consulted Hooke on the dome’s design.  To quote from the cathedral’s website [1]:

The two half-sections [of the dome] in the study employ a formula devised by Robert Hooke in about 1671 for calculating the curve of a parabolic dome and reducing its thickness.  Hooke had explored this curve the three-dimensional equivalent of the ‘hanging chain’, or catenary arch: the shape of a weighted chain which, when inverted, produces the ideal profile for a self-supporting arch.  He thought that such a curve derived from the equation y = x3.

A figure from Wren's design of St. Paul's Cathedral. (Courtesy of the British Museum)

A figure from Wren’s design of St. Paul’s Cathedral. (Courtesy of the British Museum)

How did Hooke came about the shape for the dome?  It wasn’t until after Hooke’s death his executor provided the unencrypted solution to the anagram [2]

Ut pendet continuum flexile, sic stabit contiguum rigidum inversum

which translates to

As hangs a flexible cable so, inverted, stand the touching pieces of an arch.

In other words, the ideal shape of an arch is exactly that of a freely hanging rope, only upside down.  Hooke understood that the building materials could withstand only compression forces and not tensile forces, in direct contrast to a rope that could resist tension but would buckle under compression.  The mathematics describing the arch and the cable are in fact identical, save for a minus sign.  Consequently, you could perform a real-time simulation of an arch using a piece of string!

Bonus:  Robert published the anagram in his book describing helioscopes, simply to “fill up the vacancy of the ensuring page” [3].  On that very page among other claims, Hooke also wrote the anagram “ceiiinosssttuu” in regards to “the true theory of elasticity”.  Can you solve this riddle?

[1] https://www.stpauls.co.uk/history-collections/the-collections/architectural-archive/wren-office-drawings/5-designs-for-the-dome-c16871708
[2] Written in Latin, the ‘u’ and ‘v’ are the same letter.
[3] In truth, Hooke was likely trying to avoid being scooped by his contemporaries, notably Issac Newton.

This article was inspired by my visit to the Huntington Library.  I would like to thank Catherine Wehrey for the illustrations and help with the research.

Beware global search and replace!

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I’m old enough to remember when cutting and pasting were really done with scissors and glue (or Scotch tape). When I was a graduate student in the late 1970s, few physicists typed their own papers, and if they did they left gaps in the text, to be filled in later with handwritten equations. The gold standard of technical typing was the IBM Correcting Selectric II typewriter. Among its innovations was the correction ribbon, which allowed one to remove a typo with the touch of a key. But it was especially important for scientists that the Selectric could type mathematical characters, including Greek letters.

IBM Selectric typeballs

IBM Selectric typeballs

It wasn’t easy. Many different typeballs were available, to support various fonts and special characters. Typing a displayed equation or in-line equation usually involved swapping back and forth between typeballs to access all the needed symbols. Most physics research groups had staff who knew how to use the IBM Selectric and spent much of their time typing manuscripts.

Though the IBM Selectric was used by many groups, typewriters have unique personalities, as forensic scientists know. I had a friend who claimed he had learned to recognize telltale differences among documents produced by various IBM Selectric machines. That way, whenever he received a referee report, he could identify its place of origin.

Manuscripts did not evolve through 23 typeset versions in those days, as one of my recent papers did. Editing was arduous and frustrating, particularly for a lowly graduate student like me, who needed to beg Blanche to set aside what she was doing for Steve Weinberg and devote a moment or two to working on my paper.

It was tremendously liberating when I learned to use TeX in 1990 and started typing my own papers. (Not LaTeX in those days, but Plain TeX embellished by a macro for formatting.) That was a technological advance that definitely improved my productivity. An earlier generation had felt the same way about the Xerox machine.

But as I was reminded a few days ago, while technological advances can be empowering, they can also be dangerous when used recklessly. I was editing a very long document, and decided to make a change. I had repeatedly used $x$ to denote an n-bit string, and thought it better to use $\vec x$ instead. I was walking through the paper with the replace button, changing each $x$ to $\vec x$ where the change seemed warranted. But I slipped once, and hit the “Replace All” button instead of “Replace.” My computer curtly informed me that it had made the replacement 1011 times. Oops …

This was a revocable error. There must have been a way to undo it (though it was not immediately obvious how). Or I could have closed the file without saving, losing some recent edits but limiting the damage.

But it was late at night and I was tired. I panicked, immediately saving and LaTeXing the file. It was a mess.

Okay, no problem, all I had to do was replace every \vec x with x and everything would be fine. Except that in the original replacement I had neglected to specify “Match Case.” In 264 places $X$ had become $\vec x$, and the new replacement did not restore the capitalization. It took hours to restore every $X$ by hand, and there are probably a few more that I haven’t noticed yet.

Which brings me to the cautionary tale of one of my former graduate students, Robert Navin. Rob’s thesis had two main topics, scattering off vortices and scattering off monopoles. On the night before the thesis due date, Rob made a horrifying discovery. The crux of his analysis of scattering off vortices concerned the singularity structure of a certain analytic function, and the chapter about vortices made many references to the poles of this function. What Rob realized at this late stage is that these singularities are actually branch points, not poles!

What to do? It’s late and you’re tired and your thesis is due in a few hours. Aha! Global search and replace! Rob replaced every occurrence of “pole” in his thesis by “branch point.” Problem solved.

Except … Rob had momentarily forgotten about that chapter on monopoles. Which, when I read the thesis, had been transformed into a chapter on monobranch points. His committee accepted the thesis, but requested some changes …

Rob Navin no longer does physics, but has been very successful in finance. I’m sure he’s more careful now.