Resource Theory of Quantum States Out of Thermal Equilibrium

Fernando G. S. L. Brandão, Michał Horodecki, Jonathan Oppenheim, Joseph M. Renes, and Robert W. Spekkens
Phys. Rev. Lett. 111, 250404 – Published 18 December 2013
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Abstract

The ideas of thermodynamics have proved fruitful in the setting of quantum information theory, in particular the notion that when the allowed transformations of a system are restricted, certain states of the system become useful resources with which one can prepare previously inaccessible states. The theory of entanglement is perhaps the best-known and most well-understood resource theory in this sense. Here, we return to the basic questions of thermodynamics using the formalism of resource theories developed in quantum information theory and show that the free energy of thermodynamics emerges naturally from the resource theory of energy-preserving transformations. Specifically, the free energy quantifies the amount of useful work which can be extracted from asymptotically many copies of a quantum system when using only reversible energy-preserving transformations and a thermal bath at fixed temperature. The free energy also quantifies the rate at which resource states can be reversibly interconverted asymptotically, provided that a sublinear amount of coherent superposition over energy levels is available, a situation analogous to the sublinear amount of classical communication required for entanglement dilution.

  • Received 17 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.111.250404

© 2013 American Physical Society

Authors & Affiliations

Fernando G. S. L. Brandão1,2, Michał Horodecki3,4, Jonathan Oppenheim5, Joseph M. Renes6,7,*, and Robert W. Spekkens8

  • 1Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, Belo Horizonte, Minas Gerais 30123-970, Brazil
  • 2Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
  • 3Institute for Theoretical Physics and Astrophysics, University of Gdańsk, PL-80952, Gdańsk, Poland
  • 4National Quantum Information Centre of Gdańsk, 81-824 Sopot, Poland
  • 5Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 6Institut für Angewandte Physik, Technische Universität Darmstadt, Hochschulstrasse 4a, 64289 Darmstadt, Germany
  • 7Institut für Theoretische Physik, ETH Zurich, CH-8093 Zürich, Switzerland
  • 8Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

  • *Corresponding author. renes@phys.ethz.ch

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Issue

Vol. 111, Iss. 25 — 20 December 2013

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