# What matters to me, and why?

Students at my college asked every Tuesday. They gathered in a white, windowed room near the center of campus. “We serve,” read advertisements, “soup, bread, and food for thought.” One professor or visitor would discuss human rights, family,  religion, or another pepper in the chili of life.

I joined occasionally. I listened by the window, in the circle of chairs that ringed the speaker. Then I ventured from college into physics.

The questions “What matters to you, and why?” have chased me through physics. I ask experimentalists and theorists, professors and students: Why do you do science? Which papers catch your eye? Why have you devoted to quantum information more years than many spouses devote to marriages?

One physicist answered with another question. Chris Jarzynski works as a professor at the University of Maryland. He studies statistical mechanics—how particles typically act and how often particles act atypically; how materials shine, how gases push back when we compress them, and more.

“How,” Chris asked, “should we quantify precision?”

Chris had in mind nonequilibrium fluctuation theoremsOut-of-equilibrium systems have large-scale properties, like temperature, that change significantly.1 Examples include white-bean soup cooling at a “What matters” lunch. The soup’s temperature drops to room temperature as the system approaches equilibrium.

Nonequilibrium. Tasty, tasty nonequilibrium.

Some out-of-equilibrium systems obey fluctuation theorems. Fluctuation theorems are equations derived in statistical mechanics. Imagine a DNA molecule floating in a watery solution. Water molecules buffet the strand, which twitches. But the strand’s shape doesn’t change much. The DNA is in equilibrium.

You can grab the strand’s ends and stretch them apart. The strand will leave equilibrium as its length changes. Imagine pulling the strand to some predetermined length. You’ll have exerted energy.

How much? The amount will vary if you repeat the experiment. Why? This trial began with the DNA curled this way; that trial began with the DNA curled that way. During this trial, the water batters the molecule more; during that trial, less. These discrepancies block us from predicting how much energy you’ll exert. But suppose you pick a number W. We can form predictions about the probability that you’ll have to exert an amount W of energy.

How do we predict? Using nonequilibrium fluctuation theorems.

Fluctuation theorems matter to me, as Quantum Frontiers regulars know. Why? Because I’ve written enough fluctuation-theorem articles to test even a statistical mechanic’s patience. More seriously, why do fluctuation theorems matter to me?

Fluctuation theorems fill a gap in the theory of statistical mechanics. Fluctuation theorems relate nonequilibrium processes (like the cooling of soup) to equilibrium systems (like room-temperature soup). Physicists can model equilibrium. But we know little about nonequilibrium. Fluctuation theorems bridge from the known (equilibrium) to the unknown (nonequilibrium).

Experiments take place out of equilibrium. (Stretching a DNA molecule changes the molecule’s length.) So we can measure properties of nonequilibrium processes. We can’t directly measure properties of equilibrium processes, which we can’t perform experimentally. But we can measure an equilibrium property indirectly: We perform nonequilibrium experiments, then plug our data into fluctuation theorems.

Which equilibrium property can we infer about? A free-energy difference, denoted by ΔF. Every equilibrated system (every room-temperature soup) has a free energy F. F represents the energy that the system can exert, such as the energy available to stretch a DNA molecule. Imagine subtracting one system’s free energy, F1, from another system’s free energy, F2. The subtraction yields a free-energy difference, ΔF = F2 – F1. We can infer the value of a ΔF from experiments.

How should we evaluate those experiments? Which experiments can we trust, and which need repeating?

Those questions mattered little to me, before I met Chris Jarzynski. Bridging equilibrium with nonequilibrium mattered to me, and bridging theory with experiment. Not experimental nitty-gritty.

I deserved a dunking in white-bean soup.

Suppose you performed infinitely many trials—stretched a DNA molecule infinitely many times. In each trial, you measured the energy exerted. You processed your data, then substituted into a fluctuation theorem. You could infer the exact value of ΔF.

But we can’t perform infinitely many trials. Imprecision mars our inference about ΔF. How does the imprecision relate to the number of trials performed?2

Chris and I adopted an information-theoretic approach. We quantified precision with a parameter $\delta$. Suppose you want to estimate ΔF with some precision. How many trials should you expect to need to perform? We bounded the number $N_\delta$ of trials, using an entropy. The bound tightens an earlier estimate of Chris’s. If you perform $N_\delta$ trials, you can estimate ΔF with a percent error that we estimated. We illustrated our results by modeling a gas.

I’d never appreciated the texture and richness of precision. But richness precision has: A few decimal places distinguish Albert Einstein’s general theory of relativity from Isaac Newton’s 17th-century mechanics. Particle physicists calculate constants of nature to many decimal places. Such a calculation earned a nod on physicist Julian Schwinger’s headstone. Precision serves as the bread and soup of much physics. I’d sniffed the importance of precision, but not tasted it, until questioned by Chris Jarzynski.

The questioning continues. My college has discontinued its “What matters” series. But I ask scientist after scientist—thoughtful human being after thoughtful human being—“What matters to you, and why?” Asking, listening, reading, calculating, and self-regulating sharpen my answers those questions. My answers often squish beneath the bread knife in my cutlery drawer of criticism. Thank goodness that repeating trials can reduce our errors.

1Or large-scale properties that will change. Imagine connecting the ends of a charged battery with a wire. Charge will flow from terminal to terminal, producing a current. You can measure, every minute, how quickly charge is flowing: You can measure how much current is flowing. The current won’t change much, for a while. But the current will die off as the battery nears depletion. A large-scale property (the current) appears constant but will change. Such a capacity to change characterizes nonequilibrium steady states (NESSes). NESSes form our second example of nonequilibrium states. Many-body localization forms a third, quantum example.

2Readers might object that scientists have tools for quantifying imprecision. Why not apply those tools? Because ΔF equals a logarithm, which is nonlinear. Other authors’ proposals appear in references 1-13 of our paper. Charlie Bennett addressed a related problem with his “acceptance ratio.” (Bennett also blogged about evil on Quantum Frontiers last month.)

# Quantum Information: Episode II: The Tools’ Applications

Monday dawns. Headlines report that “Star Wars: Episode VII” has earned more money, during its opening weekend, than I hope to earn in my lifetime. Trading the newspaper for my laptop, I learn that a friend has discovered ThinkGeek’s BB-8 plushie. “I want one!” she exclaims in a Facebook post. “Because BB-8 definitely needs to be hugged.”

BB-8 plays sidekick to Star Wars hero Poe Dameron. The droid has a spherical body covered with metallic panels and lights.Mr. Gadget and Frosty the Snowman could have spawned such offspring. BB-8 has captured viewers’ hearts, and its chirps have captured cell-phone ringtones.

ThinkGeek’s BB-8 plushie

Still, I scratch my head over my friend’s Facebook post. Hugged? Why would she hug…

Oh. Oops.

I’ve mentally verbalized “BB-8” as “BB84.” BB84 denotes an application of quantum theory to cryptography. Cryptographers safeguard information from eavesdroppers and tampering. I’ve been thinking that my friend wants to hug a safety protocol.

Charles Bennett and Gilles Brassard invented BB84 in 1984. Imagine wanting to tell someone a secret. Suppose I wish to coordinate, with a classmate, the purchase of a BB-8 plushie for our friend the droid-hugger. Suppose that the classmate and I can communicate only via a public channel on which the droid-hugger eavesdrops.

Cryptographers advise me to send my classmate a key. A key is a random string of letters, such as CCCAAACCABACA. I’ll encode my message with the string, with which my classmate will decode the message.

I have to transmit the key via the public channel. But the droid-hugger eavesdrops on the public channel. Haven’t we taken one step forward and one step back? Why would the key secure our information?

Because quantum-information science enables me to to transmit the key without the droid-hugger’s obtaining it. I won’t transmit random letters; I’ll transmit quantum states. That is, I’ll transmit physical systems, such as photons (particles of light), whose properties encode quantum information.

A nonquantum letter has a value, such as A or B or C.  Each letter has one and only one value, regardless of whether anyone knows what value the letter has. You can learn the value by measuring (looking at) the letter. We can’t necessarily associate such a value with a quantum state. Imagine my classmate measuring a state I send. Which value the measurement device outputs depends on chance and on how my classmate looks at the state.

If the droid-hugger intercepts and measures the state, she’ll change it. My classmate and I will notice such changes. We’ll scrap our key and repeat the BB84 protocol until the droid-hugger quits eavesdropping.

BB84 launched quantum cryptography, the safeguarding of information with quantum physics. Today’s quantum cryptographers rely on BB84 as you rely, when planning a holiday feast, on a carrot-cake recipe that passed your brother’s taste test on his birthday. Quantum cryptographers construct protocols dependent on lines like “The message sender and receiver are assumed to share a key distributed, e.g., via the BB84 protocol.”

BB84 has become a primitive task, a solved problem whose results we invoke in more-complicated problems. Other quantum-information primitives include (warning: jargon ahead) entanglement distillation, entanglement dilution, quantum data compression, and quantum-state merging. Quantum-information scientists solved many primitive problems during the 1990s and early 2000s. You can apply those primitives, even if you’ve forgotten how to prove them.

A primitive task, like quantum-entanglement distillation

Those primitives appear to darken quantum information’s horizons. The spring before I started my PhD, an older physicist asked me why I was specializing in quantum information theory. Haven’t all the problems been solved? he asked. Isn’t quantum information theory “dead”?

Imagine discovering how to power plasma blades with kyber crystals. Would you declare, “Problem solved” and relegate your blades to the attic? Or would you apply your tool to defending freedom?

Primitive quantum-information tools are unknotting problems throughout physics—in computer science; chemistry; optics (the study of light); thermodynamics (the study of work, heat, and efficiency); and string theory. My advisor has tracked how uses of “entanglement,” a quantum-information term, have swelled in high-energy-physics papers.

A colleague of that older physicist views quantum information theory as a toolkit, a perspective, a lens through which to view science. During the 1700s, the calculus invented by Isaac Newton and Gottfried Leibniz revolutionized physics. Emmy Noether (1882—1935) recast physics in terms of symmetries and conservation laws. (If the forces acting on a system don’t change in time, for example, the system doesn’t gain or lose energy. A constant force is invariant under, or symmetric with respect to, the progression of time. This symmetry implies that the system’s energy is conserved.) We can cast physics instead (jargon ahead) in terms of the minimization of a free energy or an action.

Quantum information theory, this physicist predicted, will revolutionize physics as calculus, symmetries, conservation, and free energy have. Quantum-information tools such as entropies, entanglement, and qubits will bleed into subfields of physics as Lucasfilm has bled into the fanfiction, LEGO, and Halloween-costume markets.

BB84, and the solution of other primitives, have not killed quantum information. They’ve empowered it to spread—thankfully, to this early-career quantum information scientist. Never mind BB-8; I’d rather hug BB84. Perhaps I shall. Engineers have realized technologies that debuted on Star Trek; quantum mechanics has secured key sharing; bakers have crafted cakes shaped like the Internet; and a droid’s popularity rivals R2D2’s. Maybe next Monday will bring a BB84 plushie.

The author hugging the BB84 paper and a plushie. On my wish list: a combination of the two.

# IQIM Presents …”my father”

Debaleena Nandi at Caltech

Following the IQIM teaser, which was made with the intent of creating a wider perspective of the scientist, to highlight the normalcy behind the perception of brilliance and to celebrate the common human struggles to achieve greatness, we decided to do individual vignettes of some of the characters you saw in the video.

We start with Debaleena Nandi, a grad student in Prof Jim Eisenstein’s lab, whose journey from Jadavpur University in West Bengal, India to the graduate school and research facility at the Indian institute of Science, Bangalore, to Caltech has seen many obstacles. We focus on the essentials of an environment needed to manifest the quest for “the truth” as Debaleena says. We start with her days as a child when her double-shift working father sat by her through the days and nights that she pursued her homework.

She highlights what she feels is the only way to growth; working on what is lacking, to develop that missing tool in your skill set, that asset that others might have by birth but you need to inspire by hard work.

Debaleena’s motto: to realize and face your shortcomings is the only way to achievement.

As we build Debaleena up, we also build up the identity of Caltech through its breathtaking architecture that oscillates from Spanish to Goth to modern. Both Debaleena and Caltech are revealed slowly, bit by bit.

This series is about dissecting high achievers, seeing the day to day steps, the bit by bit that adds up to the more often than not, overwhelming, impressive presence of Caltech’s science. We attempt to break it down in smaller vignettes that help us appreciate the amount of discipline, intent and passion that goes into making cutting edge researchers.

Presenting the emotional alongside the rational is something this series aspires to achieve. It honors and celebrates human limitations surrounding limitless boundaries, discoveries and possibilities.

Stay tuned for more vignettes in the IQIM Presents “My _______” Series.

But for now, here is the video. Watch, like and share!

(C) Parveen Shah Production 2014

# Squeezing light using mechanical motion

This post is about generating a special type of light, squeezed light, using a mechanical resonator. But perhaps more importantly, it’s about an experiment (Caltech press release can be found here) that is very close to my heart: an experiment that brings to an end my career as a graduate student at Caltech and the IQIM, while paying homage to nearly four decades of work done by those before me at this institute.

The Quantum Noise of Light

First of all, what is squeezed light? It would be silly of me to imagine that I can provide a more clear and thorough explanation than what Jeff Kimble gave twenty years ago in Caltech’s Engineering and Science magazine. Instead, I’ll try to present what squeezing is in the context of optomechanics.

Quantization of light makes it noisy. Imagine a steady stream of water hitting a plate, and rolling off of it smoothly. The stream would indeed impart a steady force on the plate, but wouldn’t really cause it to “shake” around much. The plate would sense a steady pressure. This is what the classical theory of light, as proposed by James Clerk Maxwell, predicts. The effect is called radiation pressure. In the early 20th century, a few decades after this prediction, quantum theory came along and told us that “light is made of photons”. More or less, this means that a measurement capable of measuring the energy, power, or pressure imparted by light, if sensitive enough, will detect “quanta”, as if light were composed of particles. The force felt by a mirror is exactly this sort of measurement. To make sense of this, we can replace that mental image of a stream hitting a plate with one of the little raindrops hitting it, where each raindrop is a photon. Since the photons are coming in one at a time, and imparting their momentum all at once in little packets, they generate a new type of noise due to their random arrival times. This is called shot-noise (since the photons act as little “shots”). Since shot-noise is being detected here by the sound it generates due to the pressure imparted by light, we call it “Radiation Pressure Shot-Noise” (RPSN).

# Grad student life: high highs and low lows

Conference for Undergraduate Women in Physics, Caltech, 19 January 2013.

On January 18-20, Caltech was one of the host campuses for the annual Conference for Undergraduate Women in Physics. Nearly 200 women attended here, mostly physics majors from the western US. It was an exciting and fun event, packed with talks, panel discussions, lab tours, a poster session, and other activities.

One highlight was a screening of The PhD Movie, followed by a discussion with director Jorge Cham and the cast (real-life Caltech grad students Alex Lockwood and Crystal Dilworth, and undergrad Raj Katti). The movie, filmed on location at Caltech, provides a very funny look at the misery of graduate student life. You can get a pretty accurate impression of the movie’s tone by viewing the trailer. The discussion afterward featured poignant warnings about the pitfalls of graduate school, and emphasized the importance of having the right mentor.

I found myself reflecting on my own experience. Graduate school will sometimes deal grave blows to your self confidence, but it can also be a time of exhilarating intellectual growth. The highs are high but the lows are low.

One thing we try to do at Quantum Frontiers is provide a variety of perspectives on the graduate student experience by featuring our students as contributors. Today we’ll try something a bit different: a profile of grad student Debaleena Nandi from Caltech writer Ann Wendland.

Of Bravery, Support, and Breakthroughs
By Ann Wendland

Debaleena Nandi, in the lab as usual.

In March 2008, a graduate student at the Indian Institute of Science (IISc) named Debaleena Nandi heard Caltech physics professor Jim Eisenstein give a series of lectures on two-dimensional systems of quantum electronic matter. “I was very keen to take a peek into his lab,” she says—so keen that, with a friend by her side for moral support, she walked up to Eisenstein and asked if she could join his group for the summer. Eisenstein had noted her smart questions during his talks and said he was open to the idea. Still, he was surprised when he returned to Caltech and found she’d e-mailed him. A few months later, Nandi rented an apartment in Pasadena and left India for the first time.