About Nicole Yunger Halpern

I recently completed a physics PhD with the buccaneers of Quantum Frontiers. Starting in Sept. 2018, I'll work as an ITAMP Postdoctoral Fellow at the Harvard-Smithsonian Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP). You'll be able to catch me at ITAMP, in Harvard's physics department, or at MIT. My research consists of what I like to call "quantum steampunk": I combine quantum information with thermodynamics, contributing to the theory of quantum thermodynamics and applying quantum thermodynamics across science. Before beginning my PhD at Caltech, I studied at Dartmouth College and the Perimeter Institute for Theoretical Physics. I like my quantum information physical, my math algebraic, and my spins rotated but not stirred.

“Methinks, I know one kind like you.”

I was expecting to pore over a poem handwritten by one of history’s most influential chemists. Sir Humphry Davy lived in Britain around the turn of the 19th century. He invented a lamp that saved miners’ lives, discovered and isolated chemical elements, coined the term “laughing gas,” and inspired younger researchers through public lectures.


Humphry Davy

Davy wrote not only scientific papers, but also poetry. He befriended contemporaries known today as “Romantic poets,” including Samuel Taylor Coleridge. English literature and the history of science rank among the specialties of the Huntington Library in San Marino, CA. The Huntington collects manuscripts and rare books, and I secured a reader card this July. I aspired to find a poem by Davy.

Bingo: The online catalogue contained an entry entitled “To the glow worm.” I requested the manuscript and settled into the hushed, wood-paneled reading room.

Davy had written scarcely legibly, in black ink, on a page that had creased and torn. I glanced over the lines, then realized that the manuscript folder contained two other pages. The pages had stuck together, so I gently flipped the lot over.

Davy poem

Poem “To the glow worm,” by Humphry Davy

A line at the top of the back page seized the wheel of my attention.

“Methinks, I know one kind like you.”

The line’s intimacy arrested me. I heard a speaker contemplating someone whom he or she had met recently, turning the person over in the speaker’s mind, gaining purchase on the person’s identity. “I know you,” I heard the speaker saying, and I saw the speaker wagging a finger at the person. “I know your type…I think.”

The line’s final six words suggested impulsiveness. How can you know someone you’re still wrapping your head around? I felt inclined to suggest a spoonful of circumspection. But perhaps the speaker was reflecting more than I’d allowed: “Methinks” suggested temperance, an acknowledgement of uncertainty.

I backpedaled to the folder’s cover. “Includes verse and letter by Lady Davy,” it read. Jane Apreece, a wealthy widow, acquired the title Lady Davy upon marrying Sir Humphry. She enjoyed a reputation for social savvy, fashionableness, and sharpness. I’d intruded on her poem, a response to Davy’s. Apreece’s pages begged for a transcription, which I struggled through until the reading room closed 45 minutes later. Dan Lewis, the Huntington’s Dibner Senior Curator of the History of Science and Technology, later improved upon my attempt (parenthesized text ours):

Methinks, I know one kind like you,

Thine(?) to peace, & Nature true;

Kindled by Feeling’s purest flame,

In Storm, or Calm, for ages(?) the same.

Bestowing most its brilliant Light,

Amidst the tranquil shades of Night;

And prompt to solace, raise, & cheer(?),

The heart, subdued by Doubt or Care.

Though not of busy Life afraid

Yet loving best, the pastoral Shade;

Shedding a Ray, more clear & pure,

A Ray, which longer shall endure,

As Friendships light must ever prove

More steadfast than the Flame of Love.

Light recurs throughout the verse: The speaker refers to two flames, to a “Ray,” and to a “brilliant Light // Amidst the tranquil shades of Night.” Comparisons with light suit a scientist, who reveals aspects of nature never witnessed before. (I expect that the speaker directs the apostrophe toward Davy.) Comparisons with light suit Davy not only professionally, but also, to Apreece, personally: Each member of the couple inspired the other to learn. Their poems reflect their intellectual symbiosis: Apreece’s references to light complement the glow worm, which Davy called “lively living lamp of night.”

The final two lines arrested me as the first line did. The speaker contrasts “Friendship[’]s light” with “the Flame of Love.” Finite resources can’t sustain flames, which consume candles, wood, and oxygen. Once its fuel disappears, flame proves less than “steadfast.” Similarly, love can’t survive on passion’s flames. Love should rest on friendship, which sheds the “light” extolled throughout the poem. Light enhances our vision, providing the wisdom needed to sustain love throughout life’s vicissitudes. 

These two lines reveal the temperance hinted at by the “Methinks.” The speaker argues for levelheadedness, for balancing emotion with sustainability. Spoonful of circumspection retracted.


The clock struck 4:45, and readers began returning their manuscripts and books to the circulation desk. I stood up—and pricked myself on a thorn of realization. The catalogue dated the manuscript to “perhaps [ . . . ] 1811 – they [Davy and Apreece] were married in 1812.” The lovers exchanged these poems without knowing that their marriage would sour years later. I’d read about their relationship—as about Davy’s science and poetry—in Richard Holmes’s The Age of Wonder. 

At least the Davys reunited when Sir Humphry’s last illness struck. At least they remained together until he died. At least a reader can step, through the manuscript, into the couple’s patch of happiness. One can hope see more clearly for their—a scientist’s, a societal navigator’s, and two human beings’—light.

Jane letter + p.1 of poem.JPG

Letter and poem by Jane Apreece (p. 1). The top segment constitutes a letter written “by Lady Davy to a ‘Miss Talbot’ (1852, January 2),” according to the catalogue.

Jane poem, p. 2.JPG

Poem by Jane Apreece (p. 2)

If anyone has insights or has corrections to the transcription, please comment. I haven’t transcribed Davy’s poem, which might illuminate Lady Davy’s response.

With thanks to the Huntington Library of San Marino, CA, for the use of its collection. With thanks to Dan Lewis for improving upon my transcription and for prodding, for five years, toward a reader card.

Doctrine of the (measurement) mean

Don’t invite me to dinner the night before an academic year begins.

You’ll find me in an armchair or sitting on my bed, laptop on my lap, journaling. I initiated the tradition the night before beginning college. I take stock of the past year, my present state, and hopes for the coming year.

Much of the exercise fosters what my high-school physics teacher called “an attitude of gratitude”: I reflect on cities I’ve visited, projects firing me up, family events attended, and subfields sampled. Other paragraphs, I want off my chest: Have I pushed this collaborator too hard or that project too little? Miscommunicated or misunderstood? Strayed too far into heuristics or into mathematical formalisms?

If only the “too much” errors, I end up thinking, could cancel the “too little.”

In one quantum-information context, they can.


Imagine that you’ve fabricated the material that will topple steel and graphene; let’s call it a supermetatopoconsulator. How, you wonder, do charge, energy, and particles move through this material? You’ll learn by measuring correlators.

A correlator signals how much, if you poke this piece here, that piece there responds. At least, a two-point correlator does: \langle A(0) B(\tau) \rangle. A(0) represents the poke, which occurs at time t = 0. B(\tau) represents the observable measured there at t = \tau. The \langle . \rangle encapsulates which state \rho the system started in.

Condensed-matter, quantum-optics, and particle experimentalists have measured two-point correlators for years. But consider the three-point correlator \langle A(0) B(\tau) C (\tau' ) \rangle, or a k-point \langle \underbrace{ A(0) \ldots M (\tau^{(k)}) }_k \rangle, for any k \geq 2. Higher-point correlators relate more-complicated relationships amongst events. Four-pointcorrelators associated with multiple times signal quantum chaos and information scrambling. Quantum information scrambles upon spreading across a system through many-body entanglement. Could you measure arbitrary-point, arbitrary-time correlators?

New material

Supermetatopoconsulator (artist’s conception)

Yes, collaborators and I have written, using weak measurements. Weak measurements barely disturb the system being measured. But they extract little information about the measured system. So, to measure a correlator, you’d have to perform many trials. Moreover, your postdocs and students might have little experience with weak measurements. They might not want to learn the techniques required, to recalibrate their detectors, etc. Could you measure these correlators easily?

Yes, if the material consists of qubits,2 according to a paper I published with Justin Dressel, José Raúl González Alsonso, and Mordecai Waegell this summer. You could build such a system from, e.g., superconducting circuits, trapped ions, or quantum dots.

You can measure \langle \underbrace{ A(0) B (\tau') C (\tau'') \ldots M (\tau^{(k)}) }_k \rangle, we show, by measuring A at t = 0, waiting until t = \tau', measuring B, and so on until measuring M at t = \tau^{(k)}. The t-values needn’t increase sequentially: \tau'' could be less than \tau', for instance. You’d have to effectively reverse the flow of time experienced by the qubits. Experimentalists can do so by, for example, flipping magnetic fields upside-down.

Each measurement requires an ancilla, or helper qubit. The ancilla acts as a detector that records the measurement’s outcome. Suppose that A is an observable of qubit #1 of the system of interest. You bring an ancilla to qubit 1, entangle the qubits (force them to interact), and look at the ancilla. (Experts: You perform a controlled rotation on the ancilla, conditioning on the system qubit.)

Each trial yields k measurement outcomes. They form a sequence S, such as (1, 1, 1, -1, -1, \ldots). You should compute a number \alpha, according to a formula we provide, from each measurement outcome and from the measurement’s settings. These numbers form a new sequence S' = \mathbf{(} \alpha_S(1), \alpha_S(1), \ldots \mathbf{)}. Why bother? So that you can force errors to cancel.

Multiply the \alpha’s together, \alpha_S(1) \times \alpha_S(1) \times \ldots, and average the product over the possible sequences S. This average equals the correlator \langle \underbrace{ A(0) \ldots M (\tau^{(k)}) }_k \rangle. Congratulations; you’ve characterized transport in your supermetatopoconsulator.


When measuring, you can couple the ancillas to the system weakly or strongly, disturbing the system a little or a lot. Wouldn’t strong measurements perturb the state \rho whose properties you hope to measure? Wouldn’t the perturbations by measurements one through \ell throw off measurement \ell + 1?

Yes. But the errors introduced by those perturbations cancel in the average. The reason stems from how we construct \alpha’s: Our formula makes some products positive and some negative. The positive and negative terms sum to zero.

Balance 2

The cancellation offers hope for my journal assessment: Errors can come out in the wash. Not of their own accord, not without forethought. But errors can cancel out in the wash—if you soap your \alpha’s with care.


1and six-point, eight-point, etc.

2Rather, each measured observable must square to the identity, e.g., A^2 = 1. Qubit Pauli operators satisfy this requirement.


With apologies to Aristotle.

I get knocked down…

“You’ll have to have a thick skin.”

Marcelo Gleiser, a college mentor of mine, emailed the warning. I’d sent a list of physics PhD programs and requested advice about which to attend. Marcelo’s and my department had fostered encouragement and consideration.

Suit up, Marcelo was saying.

Criticism fuels science, as Oxford physicist David Deutsch has written. We have choices about how we criticize. Some criticism styles reflect consideration for the criticized work’s creator. Tufts University philosopher Daniel Dennett has devised guidelines for “criticizing with kindness”:1

1. You should attempt to re-express your target’s position so clearly, vividly, and fairly that your target says, “Thanks, I wish I’d thought of putting it that way.

2. You should list any points of agreement (especially if they are not matters of general or widespread agreement).

3. You should mention anything you have learned from your target.

4. Only then are you permitted to say so much as a word of rebuttal or criticism.

Scientists skip to step four often—when refereeing papers submitted to journals, when posing questions during seminars, when emailing collaborators, when colleagues sketch ideas at a blackboard. Why? Listening and criticizing require time, thought, and effort—three of a scientist’s most valuable resources. Should any scientist spend those resources on an idea of mine, s/he deserves my gratitude. Spending empathy atop time, thought, and effort can feel supererogatory. Nor do all scientists prioritize empathy and kindness. Others of us prioritize empathy but—as I have over the past five years—grown so used to its latency, I forget to demonstrate it.

Doing science requires facing not only criticism, but also “That doesn’t make sense,” “Who cares?” “Of course not,” and other morale boosters.

Doing science requires resilience.


So do measurements of quantum information (QI) scrambling. Scrambling is a subtle, late, quantum stage of equilibration2 in many-body systems. Example systems include chains of spins,3 such as in ultracold atoms, that interact with each other strongly. Exotic examples include black holes in anti-de Sitter space.4

Imagine whacking one side of a chain of interacting spins. Information about the whack will disseminate throughout the chain via entanglement.5 After a long interval (the scrambling time, t_*), spins across the systems will share many-body entanglement. No measurement of any few, close-together spins can disclose much about the whack. Information will have scrambled across the system.

QI scrambling has the subtlety of an assassin treading a Persian carpet at midnight. Can we observe scrambling?


A Stanford team proposed a scheme for detecting scrambling using interferometry.6 Justin Dressel, Brian Swingle, and I proposed a scheme based on weak measurements, which refrain from disturbing the measured system much. Other teams have proposed alternatives.

Many schemes rely on effective time reversal: The experimentalist must perform the quantum analog of inverting particles’ momenta. One must negate the Hamiltonian \hat{H}, the observable that governs how the system evolves: \hat{H} \mapsto - \hat{H}.

At least, the experimentalist must try. The experimentalist will likely map \hat{H} to - \hat{H} + \varepsilon. The small error \varepsilon could wreak havoc: QI scrambling relates to chaos, exemplified by the butterfly effect. Tiny perturbations, such as the flap of a butterfly’s wings, can snowball in chaotic systems, as by generating tornadoes. Will the \varepsilon snowball, obscuring observations of scrambling?


It needn’t, Brian and I wrote in a recent paper. You can divide out much of the error until t_*.

You can detect scrambling by measuring an out-of-time-ordered correlator (OTOC), an object I’ve effused about elsewhere. Let’s denote the time-t correlator by F(t). You can infer an approximation \tilde{F}(t) to F(t) upon implementing an \varepsilon-ridden interferometry or weak-measurement protocol. Remove some steps from that protocol, Brian and I say. Infer a simpler, easier-to-measure object \tilde{F}_{\rm simple}(t). Divide the two measurement outcomes to approximate the OTOC:

F(t)  \approx \frac{ \tilde{F}(t) }{ \tilde{F}_{\rm simple}(t) }.

OTOC measurements exhibit resilience to error.

Arm 2

Physicists need resilience. Brian criticizes with such grace, he could serve as the poster child for Daniel Dennett’s guidelines. But not every scientist could. How can we withstand kindness-lite criticism?

By drawing confidence from what we’ve achieved, with help from mentors like Marcelo. I couldn’t tell what about me—if anything—could serve as a rock on which to plant a foot, as an undergrad. Mentors identified what I had too little experience to appreciate. You question what you don’t understand, they said. You assimilate perspectives from textbooks, lectures, practice problems, and past experiences. You scrutinize details while keeping an eye on the big picture. So don’t let so-and-so intimidate you.

I still lack my mentors’ experience, but I’ve imbibed a drop of their insight. I savor calculations that I nail, congratulate myself upon nullifying referees’ concerns, and celebrate the theorems I prove.

I’ve also created an email folder entitled “Nice messages.” In go “I loved your new paper; combining those topics was creative,” “Well done on the seminar; I’m now thinking of exploring that field,” and other rarities. The folder affords an umbrella when physics clouds gather.

Finally, I try to express appreciation of others’ work.7 Science thrives on criticism, but scientists do science. And scientists are human—undergrads, postdocs, senior researchers, and everyone else.

Doing science—and attempting to negate Hamiltonians—we get knocked down. But we can get up again.


Around the time Brian and I released “Resilience” two other groups proposed related renormalizations. Check out their schemes here and here.

1Thanks to Sean Carroll for alerting me to this gem of Dennett’s.

2A system equilibrates as its large-scale properties, like energy, flatline.

3Angular-momentum-like quantum properties

4Certain space-times different from ours

5Correlations, shareable by quantum systems, stronger than any achievable by classical systems

6The cancellation (as by a crest of one wave and a trough of another) of components of a quantum state, or the addition of components (as two waves’ crests)

7Appreciation of specific qualities. “Nice job” can reflect a speaker’s belief but often reflects a desire to buoy a receiver whose work has few merits to elaborate on. I applaud that desire and recommend reinvesting it. “Nice job” carries little content, which evaporates under repetition. Specificity provides content: “Your idea is alluringly simple but could reverberate across multiple fields” has gristle.

So long, and thanks for all the Fourier transforms

The air conditioning in Caltech’s Annenberg Center for Information Science and Technology broke this July. Pasadena reached 87°F on the fourth, but my office missed the memo. The thermostat read 62°.

Hyperactive air conditioning suits a thermodynamicist’s office as jittery wifi suits an electrical-engineering building. Thermodynamicists call air conditioners “heat pumps.” A heat pump funnels heat—the energy of random motion—from cooler bodies to hotter. Heat flows spontaneously only from hot to cold on average, according to the Second Law of Thermodynamics. Pumping heat against its inclination costs work, organized energy drawn from a reliable source.

Reliable sources include batteries, coiled springs, and ACME anvils hoisted into the air. Batteries have chemical energy that power electric fans. ACME anvils have gravitational potential energy that splat coyotes.


I hoisted binder after binder onto my desk this July. The binders felt like understudies for ACME anvils, bulging with papers. They contained notes I’d written, and articles I’d read, for research throughout the past five years. My Caltech sojourn was switching off its lights and drawing its shutters. A control theorist was inheriting my desk. I had to move my possessions to an office downstairs, where I’d moonlight until quitting town.

Quitting town.

I hadn’t expected to feel at home in southern California, after stints in New and old England. But research and researchers drew me to California and then hooked me. Caltech’s Institute for Quantum Information and Matter (IQIM) has provided an intellectual home, colleagues-cum-friends, and a base from which to branch out to other scholars and institutions.

The IQIM has provided also the liberty to deck out my research program as a college dorm room with posters—according to my tastes, values, and exuberances. My thesis demanded the title “Quantum steampunk: Quantum information, thermodynamics, their intersection, and applications thereof across physics.” I began developing the concept of quantum steampunk on this blog. Writing a manifesto for the concept, in the thesis’s introduction, proved a delight:

The steampunk movement has invaded literature, film, and art over the past three decades. Futuristic technologies mingle, in steampunk works, with Victorian and wild-west settings. Top hats, nascent factories, and grimy cities counterbalance time machines, airships, and automata. The genre arguably originated in 1895, with the H.G. Wells novel The Time Machine. Recent steampunk books include the best-selling The Invention of Hugo Cabret; films include the major motion picture Wild Wild West; and artwork ranges from painting to jewelry to sculpture.

Steampunk captures the romanticism of fusing the old with the cutting-edge. Technologies proliferated during the Victorian era: locomotives, Charles Babbage’s analytical engine, factories, and more. Innovation facilitated exploration. Add time machines, and the spirit of adventure sweeps you away. Little wonder that fans flock to steampunk conventions, decked out in overcoats, cravats, and goggles.

What steampunk fans dream, quantum-information thermodynamicists live.

Thermodynamics budded during the late 1800s, when steam engines drove the Industrial Revolution. Sadi Carnot, Ludwig Boltzmann, and other thinkers wondered how efficiently engines could operate. Their practical questions led to fundamental insights—about why time flows; how much one can know about a physical system; and how simple macroscopic properties, like temperature, can capture complex behaviors, like collisions by steam particles. An idealization of steam—the classical ideal gas—exemplifies the conventional thermodynamic system. Such systems contain many particles, behave classically, and are often assumed to remain in equilibrium.

But thermodynamic concepts—such as heat, work, and equilibrium—characterize small scales, quantum systems, and out-of-equilibrium processes. Today’s experimentalists probe these settings, stretching single DNA strands with optical tweezers [4], cooling superconducting qubits to build quantum computers [5, 6], and extracting work from single-electron boxes [7]. These settings demand reconciliation with 19th-century thermodynamics. We need a toolkit for fusing the old with the new.

Quantum information (QI) theory provides such a toolkit. Quantum phenomena serve as resources for processing information in ways impossible with classical systems. Quantum computers can solve certain computationally difficult problems quickly; quantum teleportation transmits information as telephones cannot; quantum cryptography secures messages; and quantum metrology centers on high- precision measurements. These applications rely on entanglement (strong correlations between quantum systems), disturbances by measurements, quantum uncertainty, and discreteness.

Technological promise has driven fundamental insights, as in thermodynamics. QI theory has blossomed into a mathematical toolkit that includes entropies, uncertainty relations, and resource theories. These tools are reshaping fundamental science, in applications across physics, computer science, and chemistry.

QI is being used to update thermodynamics, in the field of quantum thermodynamics (QT) [8, 9]. QT features entropies suited to small scales; quantum engines; the roles of coherence in thermalization and transport; and the transduction of information into work, à la Maxwell’s demon [10].

This thesis (i) contributes to the theory of QI thermodynamics and (ii) applies the theory, as a toolkit, across physics. Spheres touched on include atomic, molecular, and optical (AMO) physics; nonequilibrium statistical mechanics; condensed matter; chemistry; and high-energy physics. I propose the name quantum steampunk for this program…

Never did I anticipate, in college, that a PhD could reflect my identity and style. I feared losing myself and my perspective in a subproblem of a subproblem of a subproblem. But I found myself blessed with the chance to name the aesthetic that’s guided my work, the scent I’ve unconsciously followed from book to class to research project to conversation, to paper, since…middle school, come to think of it. I’m grateful for that opportunity.

Q. steampunk

Whump, went my quantum-engine binder on my desk. I’d stuck an address label, pointing to Annenberg, to the binder. If the binder walked away, whoever found it would know where it belonged. Scratching at the label with a fingernail failed to budge the sticker. I stuck a label addressed to Cambridge, Massachusetts alongside the Pasadena address.

I’m grateful to be joining Harvard as an ITAMP (Institute for Theoretical Atomic, Molecular, and Optical Physics) Postdoctoral Fellow. You’ll be able to catch me in Harvard’s physics department, in ITAMP, or at MIT, starting this September.

While hunting for a Cambridge apartment, I skyped with potential roommates. I’d inquire about locations, about landlords and landladies, about tidiness, and about heating. The heating system’s pretty old, most tenants would admit. We keep the temperature between 60 and 65 degrees, to keep costs down. I’d nod and extol the layering of sweaters, but I shivered inside.

One tenant surprised me. The heating…works too well, she said. It’s pretty warm, to tell the truth. I thought about heat pumps and quantum engines, about picnics in the Pasadena sunshine, about the Julys I’d enjoyed while the world around me had sweated. Within an hour, I’d committed to sharing the apartment.


Some of you have asked whether I’ll continue blogging for Quantum Frontiers. Yes: Extricating me from the IQIM requires more than 3,000 miles.

See you in Cambridge.


With apologies to Douglas Adams.

What’s the worst that could happen?

The archaeologist Howard Carter discovered Tutankhamun’s burial site in 1922. No other Egyptian pharaoh’s tomb had survived mostly intact until the modern era. Gold and glass and faience, statues and pendants and chariots, had evaded looting. The discovery would revolutionize the world’s understanding of, and enthusiasm for, ancient Egypt.

First, the artifacts had to leave the tomb.

Tutankhamun lay in three coffins nested like matryoshka dolls. Carter describes the nesting in his book The Tomb of Tutankhamen. Lifting the middle coffin from the outer coffin raised his blood pressure:

Everything may seem to be going well until suddenly, in the crisis of the process, you hear a crack—little pieces of surface ornament fall. Your nerves are at an almost painful tension. What is happening? All available room in the narrow space is crowded by your men. What action is needed to avert a catastrophe?

In other words, “What’s the worst that could happen?”

Matryoshka dolls

Collaborators and I asked that question in a paper published last month. We had in mind less Egyptology than thermodynamics and information theory. But never mind the distinction; you’re reading Quantum Frontiers! Let’s mix the fields like flour and oil in a Biblical grain offering.

Carter’s team had trouble separating the coffins: Ancient Egyptian priests (presumably) had poured fluid atop the innermost, solid-gold coffin. The fluid had congealed into a brown gunk, gluing the gold coffin to the bottom of the middle coffin. Removing the gold coffin required work—thermodynamic work.

Work consists of “well-ordered” energy usable in tasks like levering coffins out of sarcophagi and motoring artifacts from Egypt’s Valley of the Kings toward Cairo. We can model the gunk as a spring, one end of which was fixed to the gold coffin and one end of which was fixed to the middle coffin. The work W required to stretch a spring depends on the spring’s stiffness (the gunk’s viscosity) and on the distance stretched through.

W depends also on details: How many air molecules struck the gold coffin from above, opposing the team’s effort? How quickly did Carter’s team pull? Had the gunk above Tuankhamun’s nose settled into a hump or spread out? How about the gunk above Tutankhamun’s left eye socket? Such details barely impact the work required to open a 6.15-foot-long coffin. But air molecules would strongly impact W if Tutankhamun measured a few nanometers in length. So imagine Egyptian matryoshka dolls as long as stubs of DNA.


Imagine that Carter found one million sets of these matryoshka dolls. Lifting a given set’s innermost coffin would require an amount W of work that would vary from set of coffins to set of coffins. W would satisfy fluctuation relations, equalities I’ve blogged about many times.

Fluctuation relations resemble the Second Law of Thermodynamics, which illuminates why time flows in just one direction. But fluctuation relations imply more-precise predictions about W than the Second Law does.

Some predictions concern dissipated work: Carter’s team could avoid spending much work by opening the coffin infinitesimally slowly. Speeding up would heat the gunk, roil air molecules, and more. The heating and roiling would cost extra work, called dissipated work, denoted by W_{\rm diss}.

Suppose that Carter’s team has chosen a lid-opening speed v. Consider the greatest W_{\rm diss} that the team might have to waste on any nanoscale coffin. W_{\rm diss}^{\rm worst} is proportional to each of three information-theoretic quantities, my coauthors and I proved.

For experts: Each information-theoretic quantity is an order-infinity Rényi divergence D_\infty ( X || Y). The Rényi divergences generalize the relative entropy D ( X || Y ). D quantifies how efficiently one can distinguish between probability distributions, or quantum states, X and Y on average. The average is over many runs of a guessing game.

Imagine the worst possible run, which offers the lowest odds of guessing correctly. D_\infty quantifies your likelihood of winning. We related W_{\rm diss}^{\rm worst} to a D_\infty between two statistical-mechanical phase-space distributions (when we described classical systems), to a D_\infty between two quantum states (when we described quantum systems), and to a D_\infty between two probability distributions over work quantities W (when we described systems quantum and classical).


The worst case marks an extreme. How do the extremes consistent with physical law look? As though they’ve escaped from a mythologist’s daydream.

In an archaeologist’s worst case, arriving at home in the evening could lead to the following conversation:

“How was your day, honey?”

“The worst possible.”

“What happened?”

“I accidentally eviscerated a 3.5-thousand-year-old artifact—the most valuable, best-preserved, most information-rich, most lavishly wrought ancient Egyptian coffin that existed yesterday.”

Suppose that the archaeologist lived with a physicist. My group (guided by a high-energy physicist) realized that the conversation could continue as follows:

“And how was your day?”

“Also the worst possible.”

“What happened?”

“I created a black hole.”

General relativity and high-energy physics have begun breeding with quantum information and thermodynamics. The offspring bear extremes like few other systems imaginable. I wonder what our results would have to say about those offspring.


National Geographic reprinted Carter’s The Tomb of Tutankhamen in its “Adventure Classics” series. The series title fits Tomb as a mummy’s bandages fit the mummy. Carter’s narrative stretches from Egypt’s New Kingdom (of 3.5 thousand years ago) through the five-year hunt for the tomb (almost fruitless until the final season), to a water boy’s discovery of steps into the tomb, to the unsealing of the burial chamber, to the confrontation of Tutankhamun’s mummy.

Carter’s book guided me better than any audio guide could have at the California Science Center. The center is hosting the exhibition “King Tut: Treasures of the Golden Pharaoh.” After debuting in Los Angeles, the exhibition will tour the world. The tour showcases 150 artifacts from Tutankhamun’s tomb.

Those artifacts drove me to my desk—to my physics—as soon as I returned home from the museum. Tutankhamun’s tomb, Carter argues in his book, ranks amongst the 20th century’s most important scientific discoveries. I’d seen a smidgeon of the magnificence that Carter’s team— with perseverance, ingenuity, meticulousness, and buckets of sweat shed in Egypt’s heat—had discovered. I don’t expect to discover anything a tenth as magnificent. But how can a young scientist resist trying?

People say, “Prepare for the worst. Hope for the best.” I prefer “Calculate the worst. Hope and strive for a Tutankhamun.”

Outside exhibition

Postscript: Carter’s team failed to unglue the gold coffin by just “stretching” the gunky “spring.” The team resorted to heat, a thermodynamic quantity alternative to work: The team flipped the middle coffin upside-down above a heat lamp. The lamp raised the temperature to 932°F, melting the goo. The melting, with more work, caused the gold coffin to plop out of the middle coffin.

A finger painting for John Preskill

I’d completed about half my candidacy exam.

Four Caltech faculty members sat in front of me, in a bare seminar room. I stood beside a projector screen, explaining research I’d undertaken. The candidacy exam functions as a milepost in year three of our PhD program. The committee confirms that the student has accomplished research and should continue.

I was explaining a quantum-thermodynamics problem. I reviewed the problem’s classical doppelgänger and a strategy for solving the doppelgänger. Could you apply the classical strategy in the quantum problem? Up to a point. Beyond it, you’d need


“Does anyone here like the Beatles?” I asked the committee. Three professors had never participated in an exam committee before. The question from the examinee appeared to startle them.

One committee member had participated in cartloads of committees. He recovered first, raising a hand.

The committee member—John Preskill—then began singing the Beatles song.

In the middle of my candidacy exam.

The moment remains one of the highlights of my career.


Throughout my PhD career, I’ve reported to John. I’ve emailed an update every week and requested a meeting about once a month. I sketch the work that’s firing me, relate my plans, and request feedback.

Much of the feedback, I’ve discerned over the years, condenses into aphorisms buried in our conversations. I doubt whether John has noticed his aphorisms. But they’ve etched themselves in me, and I hope they remain there.

“Think big.” What would impact science? Don’t buff a teapot if you could be silversmithing.

Education serves as “money in the bank.” Invest in yourself, and draw on the interest throughout your career.

“Stay broad.” (A stretching outward of both arms accompanies this aphorism.) Embrace connections with diverse fields. Breadth affords opportunities to think big.

“Keep it simple,” but “do something technical.” A teapot cluttered with filigree, spouts, and eighteen layers of gold leaf doesn’t merit a spot at the table. A Paul Revere does.

“Do what’s best for Nicole.” I don’t know how many requests to speak, to participate on committees, to explain portions of his lecture notes, to meet, to contribute to reports, and more John receives per week. The requests I receive must look, in comparison, like a mouse to a mammoth. But John exhorts me to to guard my time for research—perhaps, partially, because he gives so much time, including to students.

“Move on.” If you discover an opportunity, study background information for a few months, seize the opportunity, wrap up the project, and seek the next window.

John has never requested my updates, but he’s grown used to them. I’ve grown used to how meetings end. Having brought him questions, I invite him to ask questions of me.

“Are you having fun?” he says.


I tell the Beatles story when presenting that quantum-thermodynamics problem in seminars.

“I have to digress,” I say when the “Help!” image appears. “I presented this slide at a talk at Caltech, where John Preskill was in the audience. Some of you know John.” People nod. “He’s a…mature gentleman.”

I borrowed the term from the apparel industry. “Mature gentleman” means “at a distinguished stage by which one deserves to have celebrated a birthday of his with a symposium.”

Many physicists lack fluency in apparel-industry lingo. My audience members take “mature” at face value.

Some audience members grin. Some titter. Some tilt their heads from side to side, as though thinking, “Eh…”

John has impact. He’s logged boatloads of technical achievements. He has the scientific muscle of a scientific rhinoceros.

And John has fun. He doesn’t mind my posting an article about audience members giggling about him.

Friends ask me whether professors continue doing science after meriting birthday symposia, winning Nobel Prizes, and joining the National Academy of Sciences. I point to the number of papers with which John has, with coauthors, electrified physics over the past 20 years. Has coauthored because science is fun. It merits singing about during candidacy exams. Satisfying as passing the exam felt two years ago, I feel more honored when John teases me about my enthusiasm for science.


A year ago, I ate lunch with an alumnus who’d just graduated from our group. Students, he reported, have a tradition of gifting John a piece of art upon graduating. I relayed the report to another recent alumnus.

“Really?” the second alumnus said. “Maybe someone gave John a piece of art and then John invented the tradition.”

Regardless of its origin, the tradition appealed to me. John has encouraged me to blog as he’s encouraged me to do theoretical physics. Writing functions as art. And writing resembles theoretical physics: Each requires little more than a pencil, paper, and thought. Each requires creativity, aesthetics, diligence, and style. Each consists of ideas, of abstractions; each lacks substance but can outlive its creator. Let this article serve as a finger painting for John Preskill.

Thanks for five fun years.


With my PhD-thesis committee, after my thesis defense. Photo credit to Nick Hutzler, who cracked the joke that accounts for everyone’s laughing. (Left to right: Xie Chen, Fernando Brandão, John Preskill, Nicole Yunger Halpern, Manuel Endres.)

Catching up with the quantum-thermo crowd

You have four hours to tour Oxford University.

What will you visit? The Ashmolean Museum, home to da Vinci drawings, samurai armor, and Egyptian mummies? The Bodleian, one of Europe’s oldest libraries? Turf Tavern, where former president Bill Clinton reportedly “didn’t inhale” marijuana?

Felix Binder showed us a cemetery.

Of course he showed us a cemetery. We were at a thermodynamics conference.

The Fifth Quantum Thermodynamics Conference took place in the City of Dreaming Spires.Participants enthused about energy, information, engines, and the flow of time. About 160 scientists attended—roughly 60 more than attended the first conference, co-organizer Janet Anders estimated.


Weak measurements and quasiprobability distributions were trending. The news delighted me, Quantum Frontiers regulars won’t be surprised to hear.

Measurements disturb quantum systems, as early-20th-century physicist Werner Heisenberg intuited. Measure a system’s position strongly, and you forfeit your ability to predict the outcomes of future momentum measurements. Weak measurements don’t disturb the system much. In exchange, weak measurements provide little information about the system. But you can recoup information by performing a weak measurement in each of many trials, then processing the outcomes.

Strong measurements lead to probability distributions: Imagine preparing a particle in some quantum state, then measuring its position strongly, in each of many trials. From the outcomes, you can infer a probability distribution \{ p(x) \}, wherein p(x) denotes the probability that the next trial will yield position x.

Weak measurements lead analogously to quasiprobability distributions. Quasiprobabilities resemble probabilities but can misbehave: Probabilities are real numbers no less than zero. Quasiprobabilities can dip below zero and can assume nonreal values.

Do not disturb 2

What relevance have weak measurements and quasiprobabilities to quantum thermodynamics? Thermodynamics involves work and heat. Work is energy harnessed to perform useful tasks, like propelling a train from London to Oxford. Heat is energy that jiggles systems randomly.

Quantum properties obscure the line between work and heat. (Here’s an illustration for experts: Consider an isolated quantum, such as a spin chain. Let H(t) denote the Hamiltonian that evolves with the time t \in [0, t_f]. Consider preparing the system in an energy eigenstate | E_i(0) \rangle. This state has zero diagonal entropy: Measuring the energy yields E_i(0) deterministically. Considering tuning H(t), as by changing a magnetic field. This change constitutes work, we learn in electrodynamics class. But if H(t) changes quickly, the state can acquire weight on multiple energy eigenstates. The diagonal entropy rises. The system’s energetics have gained an unreliability characteristic of heat absorption. But the system has remained isolated from any heat bath. Work mimics heat.)

Quantum thermodynamicists have defined work in terms of a two-point measurement scheme: Initialize the quantum system, such as by letting heat flow between the system and a giant, fixed-temperature heat reservoir until the system equilibrates. Measure the system’s energy strongly, and call the outcome E_i. Isolate the system from the reservoir. Tune the Hamiltonian, performing the quantum equivalent of propelling the London train up a hill. Measure the energy, and call the outcome E_f.

Any change \Delta E in a system’s energy comes from heat Q and/or from work W, by the First Law of Thermodynamics, \Delta E = Q + W.  Our system hasn’t exchanged energy with any heat reservoir between the measurements. So the energy change consists of work: E_f - E_i =: W.


Imagine performing this protocol in each of many trials. Different trials will require different amounts W of work. Upon recording the amounts, you can infer a distribution \{ p(W) \}. p(W) denotes the probability that the next trial will require an amount W of work.

Measuring the system’s energy disturbs the system, squashing some of its quantum properties. (The measurement eliminates coherences, relative to the energy eigenbasis, from the state.) Quantum properties star in quantum thermodynamics. So the two-point measurement scheme doesn’t satisfy everyone.

Enter weak measurements. They can provide information about the system’s energy without disturbing the system much. Work probability distributions \{ p(W) \} give way to quasiprobability distributions \{ \tilde{p}(W) \}.

So propose Solinas and Gasparinetti, in these papers. Other quantum thermodynamicists apply weak measurements and quasiprobabilities differently.2 I proposed applying them to characterize chaos, and the scrambling of quantum information in many-body systems, at the conference.3 Feel free to add your favorite applications to the “comments” section.


All the quantum ladies: The conference’s female participants gathered for dinner one conference night.

Wednesday afforded an afternoon for touring. Participants congregated at the college of conference co-organizer Felix Binder.3 His tour evoked, for me, the ghosts of thermo conferences past: One conference, at the University of Cambridge, had brought me to the grave of thermodynamicist Arthur Eddington. Another conference, about entropies in information theory, had convened near Canada’s Banff Cemetery. Felix’s tour began with St. Edmund Hall’s cemetery. Thermodynamics highlights equilibrium, a state in which large-scale properties—like temperature and pressure—remain constant. Some things never change.



With thanks to Felix, Janet, and the other coordinators for organizing the conference.

1Oxford derives its nickname from an elegy by Matthew Arnold. Happy National Poetry Month!


3Michele Campisi joined me in introducing out-of-time-ordered correlators (OTOCs) into the quantum-thermo conference: He, with coauthor John Goold, combined OTOCs with the two-point measurement scheme.

3Oxford University contains 38 colleges, the epicenters of undergraduates’ social, dining, and housing experiences. Graduate students and postdoctoral scholars affiliate with colleges, and senior fellows—faculty members—govern the colleges.