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: Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment

Our paper Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment has appeared in Physical Review Letters.

Phys. Rev. Lett. 106, 050403 (2011) [arXiv version]

César A. Rodríguez-Rosario, Gen Kimura, Hideki Imai, and Alán Aspuru-Guzik

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.

Previously, here and here.

“The more physics you have the less engineering you need.”
-Ernest Rutherford

‘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.
-Heisenberg

International Journal of Quantum Information Call for Papers: Quantum Correlations: entanglement and beyond

Kavan Modi has asked me to share this call for papers for a special issue. It looks very exciting indeed.

CALL for PAPERS (Special Issue)
INTERNATIONAL JOURNAL of QUANTUM INFORMATION
Quantum Correlations: entanglement and beyond

GUEST EDITORS
Shunlong Luo (Chinese Academy of Sciences, CN)
Sabrina Maniscalco (Heriot-Watt University, Edinburgh, UK)
Kavan Modi (National University of Singapore, SG)
G. Massimo Palma (University of Palermo, IT)
Matteo G. A. Paris (University of Milano, IT)

Quantum correlations have been the subject of intensive studies in the last two decades, mainly due to the general belief that they are fundamental resources for quantum information processing and other
tasks in quantum technology. The first rigorous attempt to address the classification of quantum correlations was put forward by Werner, who formalized the elusive concept of quantum entanglement. More recently, other quantities, as such quantum discord, have been proposed to capture different aspects of the quantumness of correlations. In parallel, several applications where quantum, classical, hybrid correlations play a role have been suggested and implemented. Among them we mention quantum imaging, interferometry, state engineering, computing and entanglement-assisted quantum measurements.

This special issue is aimed to collect papers addressing both fundamental problems and applications, thus offering to readers comprehensive and up-to-date overview on the characterization and use
of quantum correlations.  We welcome papers that address fundamental aspects of quantum and classical correlations in discrete and continuous variable systems, propose implementations to make
quantitative measurements of quantum correlations, or describe experiments that exploit quantum correlations as a resource for quantum technology.

Possible topics include, but are in no way limited to: characterization and measurement of entanglement and quantum discord, discrimination of classical and quantum correlations in quantum systems, applications of quantum correlations to quantum technology, dynamics of quantum correlations in open systems, decoherence, metrology, error correction.

Manuscripts should be submitted to matteo.paris@fisica.unimi.it with subject “[QCSPE] and must meet the normal refereeing standards of IJQI.

LaTeX is the exceedingly preferred format, IJQI macros are available at
http://www.worldscinet.com/style_files/ijqi/187-readme_2e.shtml
Deadline for submission is May 15th 2011. Publication is expected within 2011.

Sincerely,

Kavan Modi, PhD
Centre for Quantum Technologies
National University of Singapore


“It is thermodynamics gone mad,” by Lord Kelvin, one of the founders of thermodynamics, commenting on Boltzmann’s derivation of Stefan’s law.

The Voice of God, Zeno and Bohmian Mechanics

A title doesn’t get more philosophical and mystical in a non-philosophical and non-mystical and technical paper than in this one:

Zeno Paradox for Bohmian Trajectories: The Unfolding of the Metatron by Maurice de Gosson, Basil Hiley

Some definitions not provided in the paper that might help unpack the references made in the title:

Metratron – angel in the religions of the Abrahamic tradition, many times depicted as the Voice of God.

Zeno Paradox – philosophical argument for “a watched pot never boils”, a physical phenomena in quantum mechanics.

Bohmian trajectories – a school on the interpretation of quantum mechanics, related to pilot waves theory.

However, I must stress this paper is not about philosophy or angels, it just a clever title.


God bless those pagans.
-Homer

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.

[SciRate]

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.

Quantum Stochastic Walks

It took some time with the printing proofs, but finally, the paper has been published.

Quantum stochastic walks: A generalization of classical random walks and quantum walks

We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.

Phys. Rev. A 81, 022323 (2010)

Previously: video abstract

Man, you come right out of a comic book. -Enter the Dragon

2010 is a good year (so far)

2010 has been awesome so far. I’m having a hard time keeping up with blogging all the good news.

Talks

I was in invited The Winter Meeting on Statistical Mechanics in Taxco, Mexico. What a fantastic conference! I learned a lot about many different areas in Statistical Physics, got to meet many awesome researchers, and the keynote talks were in a natural amphitheater inside the Cacahuamilpa caves. Stunning! This was one of the best conferences I’ve been to.

I was also invited to give a talk at Reed College last week. This was my first time ever in Portland, Oregon, and I fell in love with the city. It felt like a mixture of Austin, Northern California and Seattle that I really liked. The academic culture at Reed is something that should be emulated everywhere: students honestly don’t care about grades, just about learning. One thing is to hear it, and another is to witness how true it is! The physics department at Reed has the most motivated and energetic physicists I’ve ever met. Wow.

Papers:

Finally, the paper that I had mentioned before appeared in PRL:

Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation

Also, the PRA on assignment maps is out in the published wild.

Linear assignment maps for correlated system-environment states

Wetting and Spreading

Alright, I found it, the best title ever on a published paper. And it was published in Review of Modern Physics, a journal with an impact factor of 38, not any random journal.

Wetting and spreading

Daniel Bonn, Jens Eggers, Joseph Indekeu, Jacques Meunier and Etienne Rolley

Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating “wet” regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

Most of us live hoping we will get a paper published with a title this cool.