Author Archives: Nicole Yunger Halpern

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About Nicole Yunger Halpern

I’m a theoretical physicist at the Joint Center for Quantum Information and Computer Science in Maryland. My research group re-envisions 19th-century thermodynamics for the 21st century, using the mathematical toolkit of quantum information theory. We then apply quantum thermodynamics as a lens through which to view the rest of science. I call this research “quantum steampunk,” after the steampunk genre of art and literature that juxtaposes Victorian settings (à la thermodynamics) with futuristic technologies (à la quantum information). For more information, check out my book for the general public, Quantum Steampunk: The Physics of Yesterday’s Tomorrow. I earned my PhD at Caltech under John Preskill’s auspices; one of my life goals is to be the subject of one of his famous (if not Pullitzer-worthy) poems. Follow me on Twitter @nicoleyh11.

The cost and yield of moving from (quantum) state to (quantum) state

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The countdown had begun.

In ten days, I’d move from Florida, where I’d spent the summer with family, to Caltech. Unfolded boxes leaned against my dresser, and suitcases yawned on the floor. I was working on a paper. Even if I’d turned around from my desk, I wouldn’t have seen the stacked books and folded sheets. I’d have seen Lorenz curves, because I’d drawn Lorenz curves all week, and the curves seemed imprinted on my eyeballs.

Using Lorenz curves, we illustrate how much we know about a quantum state. Say you have an electron, you’ll measure it using a magnet, and you can’t predict any measurement’s outcome. Whether you orient the magnet up-and-down, left-to-right, etc., you haven’t a clue what number you’ll read out. We represent this electron’s state by a straight line from (0, 0) to (1, 1).

Uniform_state

Say you know the electron’s state. Say you know that, if you orient the magnet up-and-down, you’ll read out +1. This state, we call “pure.” We represent it by a tented curve.

Pure_state

The more you know about a state, the more the state’s Lorenz curve deviates from the straight line.

Arbitrary_state

If Curve A fails to dip below Curve B, we know at least as much about State A as about State B. We can transform State A into State B by manipulating and/or discarding information.

Conversion_yield_part_1_arrow

By the time I’d drawn those figures, I’d listed the items that needed packing. A coauthor had moved from North America to Europe during the same time. If he could hop continents without impeding the paper, I could hop states. I unzipped the suitcases, packed a box, and returned to my desk.

Say Curve A dips below Curve B. We know too little about State A to transform it into State B. But we might combine State A with a state we know lots about. The latter state, C, might be pure. We have so much information about A + C, the amalgam can turn into B.

Yet more conversion costs Yet-more-conversion-costs-part-2

What’s the least amount of information we need about C to ensure that A + C can turn into B? That number, we call the “cost of transforming State A into State B.”

We call it that usually. But late in the evening, after I’d miscalculated two transformation costs and deleted four curves, days before my flight, I didn’t type the cost’s name into emails to coauthors. I typed “the cost of turning A into B” or “the cost of moving from state to state.”
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The complementarity (not incompatibility) of reason and rhyme

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Shortly after learning of the Institute for Quantum Information and Matter, I learned of its poetry.

I’d been eating lunch with a fellow QI student at the Perimeter Institute for Theoretical Physics. Perimeter’s faculty includes Daniel Gottesman, who earned his PhD at what became Caltech’s IQIM. Perhaps as Daniel passed our table, I wondered whether a liberal-arts enthusiast like me could fit in at Caltech.

“Have you seen Daniel Gottesman’s website?” my friend replied. “He’s written a sonnet.”

Quill

He could have written equations with that quill.

Digesting this news with my chicken wrap, I found the website after lunch. The sonnet concerned quantum error correction, the fixing of mistakes made during computations by quantum systems. After reading Daniel’s sonnet, I found John Preskill’s verses about Daniel. Then I found more verses of John’s.

To my Perimeter friend: You win. I’ll fit in, no doubt.

Exhibit A: the latest edition of The Quantum Times, the newsletter for the American Physical Society’s QI group. On page 10, my enthusiasm for QI bubbles over into verse. Don’t worry if you haven’t heard all the terms in the poem. Consider them guidebook entries, landmarks to visit during a Wikipedia trek.

If you know the jargon, listen to it with a newcomer’s ear. Does anyone other than me empathize with frustrated lattices? Or describe speeches accidentally as “monotonic” instead of as “monotonous”? Hearing jargon outside its natural habitat highlights how not to explain research to nonexperts. Examining names for mathematical objects can reveal properties that we never realized those objects had. Inviting us to poke fun at ourselves, the confrontation of jargon sprinkles whimsy onto the meringue of physics.

No matter your familiarity with physics or poetry: Enjoy. And fifty points if you persuade Physical Review Letters to publish this poem’s sequel.

Quantum information

By Nicole Yunger Halpern

If “CHSH” rings a bell,
you know QI’s fared, lately, well.
Such promise does this field portend!
In Neumark fashion, let’s extend
this quantum-information spring:
dilation, growth, this taking wing.

We span the space of physics types
from spin to hypersurface hype,
from neutron-beam experiment
to Bohm and Einstein’s discontent,
from records of a photon’s path
to algebra and other math
that’s more abstract and less applied—
of platforms’ details, purified.

We function as a refuge, too,
if lattices can frustrate you.
If gravity has got your goat,
momentum cutoffs cut your throat:
Forget regimes renormalized;
our states are (mostly) unit-sized.
Velocities stay mostly fixed;
results, at worst, look somewhat mixed.

Though factions I do not condone,
the action that most stirs my bones
is more a spook than Popov ghosts; 1
more at-a-distance, less quark-close.

This field’s a tot—cacophonous—
like cosine, not monotonous.
Cacophony enlivens thought:
We’ve learned from noise what discord’s not.

So take a chance on wave collapse;
enthuse about the CP maps;
in place of “part” and “piece,” say “bit”;
employ, as yardstick, Hilbert-Schmidt;
choose quantum as your nesting place,
of all the fields in physics space.

1 With apologies to Ludvig Faddeev.

Steampunk quantum

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A dark-haired man leans over a marble balustrade. In the ballroom below, his assistants tinker with animatronic elephants that trumpet and with potions for improving black-and-white photographs. The man is an inventor near the turn of the 20th century. Cape swirling about him, he watches technology wed fantasy.

Welcome to the steampunk genre. A stew of science fiction and Victorianism, steampunk has invaded literature, film, and the Wall Street Journal. A few years after James Watt improved the steam engine, protagonists build animatronics, clone cats, and time-travel. At sci-fi conventions, top hats and blast goggles distinguish steampunkers from superheroes.

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The closest the author has come to dressing steampunk.

I’ve never read steampunk other than H. G. Wells’s The Time Machine—and other than the scene recapped above. The scene features in The Wolsenberg Clock, a novel by Canadian poet Jay Ruzesky. The novel caught my eye at an Ontario library.

In Ontario, I began researching the intersection of QI with thermodynamics. Thermodynamics is the study of energy, efficiency, and entropy. Entropy quantifies uncertainty about a system’s small-scale properties, given large-scale properties. Consider a room of air molecules. Knowing that the room has a temperature of 75°F, you don’t know whether some molecule is skimming the floor, poking you in the eye, or elsewhere. Ambiguities in molecules’ positions and momenta endow the gas with entropy. Whereas entropy suggests lack of control, work is energy that accomplishes tasks.
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This single-shot life

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The night before defending my Masters thesis, I ran out of shampoo. I ran out late enough that I wouldn’t defend from beneath a mop like Jack Sparrow’s; but, belonging to the Luxuriant Flowing-Hair Club for Scientists (technically, if not officially), I’d have to visit Shopper’s Drug Mart.

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The author’s unofficially Luxuriant Flowing Scientist Hair

Before visiting Shopper’s Drug Mart, I had to defend my thesis. The thesis, as explained elsewhere, concerns epsilons, the mathematical equivalents of seed pearls. The thesis also concerns single-shot information theory.

Ordinary information theory emerged in 1948, midwifed by American engineer Claude E. Shannon. Shannon calculated how efficiently we can pack information into symbols when encoding long messages. Consider encoding this article in the fewest possible symbols. Because “the” appears many times, you might represent “the” by one symbol. Longer strings of symbols suit misfits like “luxuriant” and “oobleck.” The longer the article, the fewer encoding symbols you need per encoded word. The encoding-to-encoded ratio decreases, toward a number called the Shannon entropy, as the message grows infinitely long.

Claude Shannon

We don’t send infinitely long messages, excepting teenagers during phone conversations. How efficiently can we encode just one article or sentence? The answer involves single-shot information theory, or—to those stuffing long messages into the shortest possible emails to busy colleagues—“1-shot info.” Pioneered within the past few years, single-shot theory concerns short messages and single trials, the Twitter to Shannon’s epic. Like articles, quantum states can form messages. Hence single-shot theory blended with quantum information in my thesis.

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Don’t sweat the epsilons…and it’s all epsilons

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I’d come to Barnes and Noble to study and to submerse in the bustle. I needed reminding that humans other than those on my history exam existed. When I ran out of tea and of names to review, I stood, stretched, and browsed the shelves. A blue-bound book caught my eye: Don’t Sweat the Small Stuff…and it’s all small stuff.

Richard Carlson wrote that book for people like me. We have packing lists, grocery lists, and laundry lists of to-do lists. We transcribe lectures. We try to rederive equations that we should just use. Call us “detail-oriented”; call us “conscientious”; we’re boring as toast, and we have earlier bedtimes. When urged to relax, we try. We might not succeed, but we try hard.

For example, I do physics instead of math. Mathematicians agonize over what-ifs: “What if this bit of the fraction reaches one while that bit goes negative and the other goes loop-the-loop? We’d be dividing by zero!” Divisions by zero atom-bomb calculations. Since dividing by a tiny number amounts to multiplying by a large number, dividing by zero amounts to multiplying by infinity. While mathematicians chew their nails over infinities, physicists often assume we needn’t. We use math to represent physical systems like pendulums and ponytails.1 Ponytails have properties, like lacking infinite masses, that don’t smack of the apocalypse. Since those properties don’t, neither does the math that represents those properties. To justify assumptions that our math “behaves nicely,” we use the jargon, “the field goes to zero at the boundary,” “the coupling’s renormalized,” and “it worked last time.”

I tried not to sweat the small stuff. I tried to shrug off the question marks at calculations’ edges. Sometimes, I succeeded. Then I began a Masters thesis about epsilons.

Self-help for calculus addicts.

In many physics problems, the Greek letter epsilon (ε) means “-ish.” The butcher sold you epsilon-close to a pound of beef? He tipped the scale a tad in your favor. Your temperature dropped from 103 to epsilon-close to normal? Stay in bed this afternoon, and you should recover by tomorrow.

For half a year, I’ve used epsilons to describe transformations between quantum states. To visualize the transformations, say you have a fistful of coins. Each coin consists of gold and aluminum. The portion of the coin that’s gold varies from coin to coin. I want a differently-sized fistful of coins, each with a certain gold content. After melting down your fistful, can you cast the fistful I want? Can you cast a fistful that’s epsilon-close to the fistful I want? I calculated answers to those questions, after substituting “quantum states” for “fistfuls” and a property called “purity” for “gold.”2

You might expect epsilon-close conversions to require less effort than exact conversions: Butchers weigh out approximately a pound of beef more quickly than they weigh a pound. But epsilon-close math requires more effort than exact math. Introducing epsilons into calculations, you introduce another number to keep track of. As that number approaches zero, approximate conversions become exact. If that number approaches zero while in a denominator, you atom-bomb calculations with infinities. The infinities remind me of geysers in a water park of quantum theory.

Have you visited a water park where geysers erupt every few minutes? Have you found a geyser head that looks dead, and crouched to check it? Epsilons resemble dead-looking geyser heads. Just as geyser heads rise only inches from the ground, epsilons have values close to zero. Say you’ve divided by epsilon, and you’re lowering its value to naught. Hitch up your swimsuit, lower your head, and squint at the faucet. Farther you crouch, and farther, till SPLAT! Water shoots up your left nostril.

Infinities have been shooting up my left nostril for months.

Rocking back on your heels, you need a towel. Dividing by an epsilon that approaches zero, I need an advisor. An advisor who knows mounds of calculus, who corrects without crushing, and who doesn’t mind my bombarding him with questions once a week. I have one, thank goodness—an advisor, not a towel.3 I wouldn’t trade him for fifty fistfuls of gold coins.

Towel in hand, I tiptoed through the water park of epsilons. I learned how quickly geysers erupt, where they appear, and how to disable some. I learned about smoothed distributions, limits superior, and Asymptotic Equipartition Properties. Though soaked after crossing the park, I survived. I submitted my thesis last week. And I have the right—should I find the chutzpah—to toss off the word “epsilonification” like a spelling-bee champ.

Had I not sweated the epsilons, I wouldn’t have finished the thesis. Should I discard Richard Carlson’s advice? I can’t say, having returned to my history review instead of reading his book. But I don’t view epsilons as troubles to sweat or not. Why not view epsilons as geysers in the water park of quantum theory? Who doesn’t work up a sweat in a park? But I wouldn’t rather leave. And maybe—if enough geysers shoot up our left nostrils—we’ll learn a smidgeon about Old Faithful.

1 I’m not kidding about ponytails.

2 Quantum whizzes: I explored a resource theory like that of pure bipartite entanglement (e.g., http://arxiv.org/abs/quant-ph/9811053). Instead of entanglement or gold, nonuniformity (distance from the maximally mixed state) is a scarce resource. The uniform (maximally mixed state) has no worth, like aluminum. This “resource theory of nonuniformity” models thermodynamic systems whose Hamiltonians are trivial (H = 0).

3 Actually, I have two advisors, and I’m grateful for both. But one helped cure my epsilons. N.B. I have not begun working at Caltech.

“Nature, you instruct me.”

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“Settle thy studies.”

Alone in his workroom, a student contemplates his future. Piles of books teeter next to him. Boxes line the walls; and glass vials, the boxes. Sunbeams that struggle through the stained-glass window illuminate dust.

The student’s name is Faust. I met him during my last winter in college, while complementing Physics 42: Introductory Quantum Mechanics with German 44: The Faust Tradition. A medieval German alchemist, Faust has inspired plays, novels, operas, the short story “The Devil and Daniel Webster” about an American Congressman, and the film “Bedazzled” starring Brendan Frasier.

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The Faust tradition in popular culture. Mephistopheles is the demon who buys Faust’s soul. (http://xkcd.com/501/)

As I wondered what to pursue a PhD in, so (roughly speaking) did Faust. In plays by Christopher Marlowe and Johann Wolfgang von Goethe, Faust wavers among law, theology, philosophy, and medicine. You’ve probably heard what happens next: Faust chooses sorcery, conjures a demon, and bargains away his soul. Hardly the role model for a college student. I preferred to keep my soul, though Maxwell’s demon had stolen my heart.

A few decades after Goethe penned Faust, English physicist James Maxwell proposed a thought experiment. Consider a box divided into two rooms, he wrote, and a demon controlling the door between the rooms. Since others have explained Maxwell’s paradox, I won’t parrot them. Suffice to say, the demon helps clarify why time flows, what knowledge is, and how information relates to matter. Quantum-information physicists, I learned in a seminar after German 44, study Maxwell’s demon. Via the demon, experiment, and math, QI physicists study the whole world. I wanted to contemplate the whole world, like Goethe’s Faust. By studying QI, I might approximate my goal. Faust, almost as much as my QI seminar, convinced me to pursue a PhD in physics.

Fast forward two years. Someone must have misread my application, because Caltech let me sign my soul to its PhD program. I am the newest Preskillite. Or Preskillnik. Whichever term, if either, irks my supervisor more.

For five years, I will haunt this blog. (Spiros will haunt me if I don’t haunt it.) I’ll try to post one article per month. Pure quantum information occupies me usually: abstract math that encodes physical effects, like entropy (a key to why time flows), decoherence (a system’s transformation from quantum to ordinary), and entanglement (one particle’s ability to affect another, instantaneously, from across a room).

In case I wax poetic about algebra, I apologize in advance. Apologies if I write too many stories about particles in boxes. In addition to training a scientist’s lens on atoms, I enjoy training it on science, culture, and communities. Tune in for scientists’ uses (and abuses) of language, why physics captivates us, and the bittersweetness of representing half our species in a roomful of male physicists (advantage: I rarely wait in line to use a physics department’s bathroom).

As I prepare to move to Caltech, a Faust line keeps replaying in my mind. It encapsulates my impression of a PhD, though written 200 years ago: “Nothing I had; and yet, enough for youth—/ delight in fiction, and the thirst for truth.”

Pleasure to meet you, Quantum Frontiers. Drink with me.