New Paper: Thermodynamics of quantum coherence

The bizarre microscopic quantum world is exemplified by Schrödinger’s cat, where a quantum mechanical “cat” state is said to be both death and alive simultaneously. This non-classical state is called a quantum coherence. Coherence is at odds with macroscopic realism. Our experience is dominated by thermodynamics, which destroys quantum coherences at our length and time scales.

We decided to study the reverse situation: In the microscopic world, can quantum coherence affect thermodynamics? We have posted a new manuscript titled “Thermodynamics of quantum coherence“.

Thermodynamics of quantum coherence [arXiv:1308.1245]
César A. Rodríguez-Rosario, Thomas Frauenheim, Alán Aspuru-Guzik

Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources. Quantum coherences seem to be a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines, affect the efficiency of quantum transport, lead to violations of Fourier’s law, and can be used to dynamically control the temperature of a state. However, the role of quantum coherence in thermodynamics is not fully understood. Here we show that the relative entropy of a state with quantum coherence with respect to its decohered state captures its deviation from thermodynamic equilibrium. As a result, changes in quantum coherence can lead to a heat flow with no associated temperature, and affect the entropy production rate. From this, we derive a quantum version of the Onsager reciprocal relations that shows that there is a reciprocal relation between thermodynamic forces from coherence and quantum transport. Quantum decoherence can be useful and offers new possibilities of thermodynamic control for quantum transport.

In this paper, we showed that quantum coherences are useful in thermodynamics in an exactly reciprocal manner to the way thermodynamics destroys coherences. This theory suggest that this interplay can lead to improved molecular devices, and to a deeper understanding of energy transport in photosynthesis.The main results of this paper include a generalization of the laws of thermodynamics and of the Onsager reciprocal relations for the quantum regime.  These allowed us to interpret quantum coherences as a new thermodynamic resource. This new theory provides a framework to unify previous results on quantum Carnot engines , thermal control by quantum measurements, quantum coherences in photosynthetic complexes and transport in molecular devices.

Open Science, or Internet Fight?

Quantum theory is the most accurate and well tested theory ever. However, it is difficult to understand without the proper mathematical background, and challenges common intuition. This makes it a target for crackpot attacks.

Scott Aaronson has gotten into a fight in his blog with the quantum denialist Joy Christian. This fight has many of the usual ingredients: angry comments, dares, misconceptions, made-up language, etc. War was declared in this post by Scott, and attacks were made in the comments to that post. This prompted Scott to follow up with a second post that is even more interesting. What makes it stand out is that 1) there is a $200,000 in line, 2) Scott has been gracious enough to study Joy’s papers, and find a central, basic and quite obvious mistake that makes the whole argument fall apart, and 3) Scott is asking for FQXi, Perimeter Institute and Oxford to cut all connections to Joy!

This has caused another debate in the comments section of the second post. Is this feeding the troll? Is this going to far? Isn’t this empowering Joy Christian more, instead of deflating him? Why pick on him, instead of any of the other quantum deniers? Even people from FQXi have posted in the blog.

Is this just another internet fight? Is this an example of what Neal Stephenson wrote in Cryptonomicon:

Arguing […] on the Internet is a sucker’s game because they almost always turn out […] to be indistinguishable from—self-righteous sixteen-year-olds possessing infinite amounts of free time.

Or is this how open science should be? After all, it does bring attention to unpublished work, focuses examination by leading researchers, and gets quick results. Just because the result invalidates the idea, was it wasted time and resources, or was it part of how open science should be done?

Is there a code of conduct for Open Science to differentiate between internet fights and good science?

Discord on Nature

A news feature in the journal Nature discusses how Quantum Discord is related to Quantum Computation. They interviewed several of my collaborators, Kavan Modi and Animesh Datta, and have a very nice summary of why it has become so fashionable lately.

Quantum Discord was first proposed by Wojciech Zurek as a measure of bipartite quantum correlations different from entanglement. As Wojciech described it to me, he presented this at a conference, and many people did not understand its significance at the time, mainly because it wasn’t clear how it related to entanglement. Meanwhile, Vlatko Vedral independently proposed a similar measure of quantum correlations. These results were both published around 2001, but Zurek’s name stuck.

A few years later, while I was in graduate school, I heard Zurek was coming to visit us in the Sudarshan group. Zurek had been a student of our department decades before, and I was very excited to meet him. I studied some of his papers, and we had a discussion that ended up on the topic of quantum discord. Although at the time I was not thinking too much about measures of quantum correlations, I was interested in the problem of initial system-environment correlations in open quantum systems.

A few months later, while walking around town lake in Austin Tx, I proposed to Kavan Modi (then a graduate student like me) and Prof. Sudarshan that the concept of classical correlations (as defined by quantum discord), might help us understand some of the issues in open quantum systems with initial correlations. That winter, Kavan and I decided to go on a road trip to New Mexico, where we visited our friend Anil Shaji, now a postdoc in Prof. Caves group. We then also met Animesh Datta. During this road trip we also visited Zurek in Los Alamos, and we had further discussions about quantum discord.

Kavan and Cesar on their way to visit Zurek to discuss Quantum Discord
Kavan and Cesar on their way to visit Zurek to discuss Quantum Discord

All these conversations led to the first paper to use quantum discord, which connected it to the mathematical properties of complete positivity of dynamical maps.

Animesh and Anil took a different direction that ultimate proved to be very useful: they noted that quantum discord was an important resource for some quantum algorithms. It was this result that has led to so many recent publications in the field.

More recently, some of us have shown how quantum discord is a fundamental dynamical characteristic of non-equilibrium thermodynamical systems.

Quantum Discord has led to advances that can be grouped into two areas: as what could become another resource in quantum computation, and as some fundamental property of the dynamics of bipartite states. Could there be a relationship between these?

‘Lazy States’ accepted in PRL

Our latest paper Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment has been accepted for publication in Physical Review Letters. Woohoo!

Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment

We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy states permits the construction of a protocol for detecting global quantum correlations using only  local dynamical information. We show how quantum correlations to the environment provide bounds to the entropy rate, and how to estimate dissipation rates for general non-Markovian open quantum systems.

I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structure nature had so generously spread out before me.

Decoherence Benasque (2)

Quantum Coherence and Decoherence 2010 at Benasque will be over tomorrow. It is a shame, the environment in this conference is very productive and has lead to many interesting discussion. I feel if I stayed a bit longer we would be able to finish some results.

I highly recommend this conference, and I think other conferences could learn a few things from the productive and laid-back atmosphere here.


Quantum Minesweeper

If you are vaguely interested in quantum mechanics, you must check out the game Quantum Minesweeper. You might want to start with the video tutorial before you play online.

The game differs from classical Minesweeper in the following ways:

  • The board is really a quantum superposition of two boards. It is your goal to figure out the superpositions. It is simplified, as only one kind of phase is allowed.
  • There are three different kind of measurements that you can do, each one a limited number of times. The measurements are:
  1. classical measurement – collapse that can trigger a mine probabilistically. Very risky!
  2. entropy measurement – it indicates if there is a superposition or not, but doesn’t tell you if there is a mine or not!
  3. interaction-free measurements – it is very magical, doesn’t collapse the wave function, actually gives you the phase information. Very powerful!

This game is fantastic!

Technical digression:

I have a question that might be a good undergraduate research project for someone interested in quantum information. What is the optimal strategy for the game? That is, if you thought of this game as a kind of state tomography problem, is there a general protocol to extract the state with high fidelity, given the constrains of the number of measurements? To make it more interesting, imagine a version of quantum minesweeper where the boards could have between them any kind of phase, how much harder would solving it be?

Give it one last try
til the next
one more
last try.
-A Wilhelm Scream

Dirac and Quantum Mechanics

Dirac invented quantum mechanics as we know it. He unified everything, adding much along the way into the modern formalism. His book from The Principles of Quantum Mechanics feels completely modern,although it was first published in 1930. However, he was also very humble, giving a lot of credit to others for things he himself discovered.

Kurt Gottfried posted a paper in arXiv:1006.4610 where he carefully examines the history of quantum mechanics by going to the original papers and getting the record straight. This highlights the central role Dirac played through out this. This cute paper is nice, with tons of references, some fun anecdotes, and just enough equations to get the details right. I highly recommend it.

Time flies like an arrow. Fruit flies like a banana.
-Groucho Marx

Why does the world look classical?

A few days ago we posted a new paper.

General Bound on the Rate of Decoherence [arXiv:10045405]

Cesar A. Rodriguez-Rosario, Gen Kimura, Hideki Imai, Alan Aspuru-Guzik

We establish the necessary and sufficient conditions for a quantum system to be stable under any general system-environment interaction. Quantum systems are stable when the time-derivative of their purity is zero. This stability provides a dynamical explanation of the classicality of measurement apparatus. We also propose a protocol to detect global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the purity rate, which in turn can be used to estimate dissipation rates for general non-Markovian open quantum systems.


The paper could have been alternatively titled: “Necessary and Sufficient Conditions for System Stability Under Any Coupling to the Environment”. In this post, I want to discuss briefly our first result of the paper:

$$left[ frac{d}{dt}mathbf{P}^mathcal{S}_tright]_{t=tau} = 0; Leftrightarrow ; left[rho^mathcal{S}_tauotimes I^mathcal{E},rho^mathcal{SE}_tauright] =0$$.

We were interested in finding universal decoherence stability criteria that depended on the structure of the system-environment state, but was independent of the particular Hamiltonian dynamics. We focused on the measure of decoherence called “Purity”, in particular the rate of change of purity. We found that there exist system-environment states that preserve the purity of the system independent of the details of the interaction Hamiltonian. These states are given by the commutator in the equation above vanishing, and we call them “Stable System States” or SSS for lack of a better name.

SSS states are sparse topologically and not-dense: they are quite rare. But, at the same time, they include states whose system part looks very classical. On first sight, since they are rare, this would raise the question of why does the world looks classical to us. However, the equation above also implies that these states are stable under decoherence, and thus can be long-lived.

In other words, we can prove how classical states emerge naturally in the world without any assumptions of the dynamics! This provides a non-equilibrium thermodynamical explanation to why our universe looks classical.

Universe as Quantum Information

Vlatko Vedral, from Oxford/CQT Singapore is promoting his new layperson book.

Decoding Reality: The Universe as Quantum Information

An infuriatingly theologically focused video interview can be found here. I’ll assume The Guardian editing is to blame.

Although I am always highly critical of all popularizations of quantum mechanics, I’ll admit I’m biased towards liking this one. Vlatko’s work on the thermodynamics of quantum information have influenced my own interests, and I’m currently working with several people in his group. I can’t wait for this book to come out.

I know it is hopeless.
Hell ain’t big enough to hold us back.
Come one, let’s pick a fight.
We hunt for trouble tonight!