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Published December 20, 2013 | Supplemental Material + Published
Journal Article Open

Resource Theory of Quantum States Out of Thermal Equilibrium

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.

Additional Information

© 2013 American Physical Society. (Received 17 August 2012; revised manuscript received 12 March 2013; published 18 December 2013) We thank Jochen Rau and Dominik Janzing for helpful conversations. J. M. R. acknowledges support from the Center for Advanced Security Research Darmstadt (CASED). R. W. S. acknowledges support from the Government of Canada through NSERC and the Province of Ontario through MRI. M. H. is grateful for the support of the Foundation for Polish Science TEAM project cofinanced by the EU European Regional Development Fund. Part of this work was done at the National Quantum Information Centre of Gdansk. The authors acknowledge the hospitality of the Institute Mittag Leffler within the program Quantum Information Science (2010), where part of this work was done.

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Published - PhysRevLett.111.250404.pdf

Supplemental Material - work-supp.pdf

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August 19, 2023
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