Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
File(s)
Published verion
Author(s)
Gour, Gilad
Jennings, D
Buscemi, Francesco
Duan, Runyao
Marvian, Iman
Type
Journal Article
Abstract
What does it mean for one quantum process to be more disordered than another? Interestingly,
this apparently abstract question arises naturally in a wide range of areas such as information the-
ory, thermodynamics, quantum reference frames and the resource theory of asymmetry. Here we
use a quantum-mechanical generalization of majorization to develop a framework for answering this
question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We
also investigate some of the applications of this framework, and remarkably find that, in the context
of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions
for arbitrary quantum state transformations under thermodynamic processes, which rigorously ac-
counts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal
processes extends thermal operations, and is based on natural physical principles, namely, energy
conservation, the existence of equilibrium states, and the requirement that quantum coherence be
accounted for thermodynamically.
this apparently abstract question arises naturally in a wide range of areas such as information the-
ory, thermodynamics, quantum reference frames and the resource theory of asymmetry. Here we
use a quantum-mechanical generalization of majorization to develop a framework for answering this
question, in terms of single-shot entropies, or equivalently, in terms of semi-definite programs. We
also investigate some of the applications of this framework, and remarkably find that, in the context
of quantum thermodynamics it provides the first complete set of necessary and sufficient conditions
for arbitrary quantum state transformations under thermodynamic processes, which rigorously ac-
counts for quantum-mechanical properties, such as coherence. Our framework of generalized thermal
processes extends thermal operations, and is based on natural physical principles, namely, energy
conservation, the existence of equilibrium states, and the requirement that quantum coherence be
accounted for thermodynamically.
Date Issued
2018-12-17
Date Acceptance
2018-08-20
Citation
Nature Communications, 2018, 9 (1)
ISSN
2041-1723
Publisher
Nature Publishing Group
Journal / Book Title
Nature Communications
Volume
9
Issue
1
Copyright Statement
© 2018 The Author(s). This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made. The images or other third party
material in this article are included in the article’s Creative Commons license, unless
indicated otherwise in a credit line to the material. If material is not included in the
article’s Creative Commons license and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder. To view a copy of this license, visit http://creativecommons.org/
licenses/by/4.0/.
Attribution 4.0 International License, which permits use, sharing,
adaptation, distribution and reproduction in any medium or format, as long as you give
appropriate credit to the original author(s) and the source, provide a link to the Creative
Commons license, and indicate if changes were made. The images or other third party
material in this article are included in the article’s Creative Commons license, unless
indicated otherwise in a credit line to the material. If material is not included in the
article’s Creative Commons license and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder. To view a copy of this license, visit http://creativecommons.org/
licenses/by/4.0/.
Subjects
Science & Technology
Multidisciplinary Sciences
Science & Technology - Other Topics
2ND LAWS
NONEQUILIBRIUM
PRINCIPLE
EVOLUTION
THEOREM
RULES
MD Multidisciplinary
Publication Status
Published
Article Number
5352
Date Publish Online
2018-12-17