Tag: technical

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.

Non-Markovian Open Quantum Systems: System-Environment Correlations in Dynamical Maps

My paper on Non-Markovian Open Quantum systems has been published in the Special Issue of International Journal of Quantum Information (IJQI):

Non-Markovian Open Quantum Systems: System-Environment Correlations in Dynamical Maps

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

This paper is an updated version of my 2008 preprint.

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.

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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

Andy Maloney’s Open Science Biophysics Dissertation

Andy Maloney, a leader in open science, is embracing the open philosophy all the way. He has decided to write his dissertation as it evolves as an open science document. First chapter draft is here. Go there to witness the first fully open dissertation ever.

Yes, every version, every draft, every correction, everything will be posted there. Members of the wiki can also write him comments and suggestions. This is a fantastic idea, as this is the first time others can see how  a dissertations actually develops. This will help both experts in the field, and graduate students that want to see how is the dissertation-writing process.

—

[Jesus walks out of the lake with a small bottle of lemonade]
Jesus Christ: Lemonade?
Father Eustace: Will there be enough?
Jesus Christ: Oh, there’ll be plenty.
-Jesus Christ Vampire Hunter

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

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

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.

Reuters Interviews Daniel Lidar

Reuter’s ScienceWatch recently posted an interview with Prof. Daniel Lidar from USC where they discuss Daniel’s most important papers, focusing on decoherence free subspaces. Daniel was very kind to mention my own work on Open Quantum Systems with initial correlations during the interview.

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“The theory of its operation is rudimentary and attempts to improve its performance are still made in an almost haphazard way”
-Sadi Carnot on engines