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Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma

Sagawa, Takahiro and Faist, Philippe and Kato, Kohtaro and Matsumoto, Keiji and Nagaoka, Hiroshi and Brandão, Fernando G. S. L. (2019) Asymptotic Reversibility of Thermal Operations for Interacting Quantum Spin Systems via Generalized Quantum Stein's Lemma. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190801-134551728

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Abstract

For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback-Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein's lemma for quantum hypothesis testing beyond independent and identically distributed (i.i.d.) situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1907.05650arXivDiscussion Paper
ORCID:
AuthorORCID
Kato, Kohtaro0000-0003-3317-2004
Nagaoka, Hiroshi0000-0002-0085-2794
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:The authors are grateful to Hiroyasu Tajima, Yoshiko Ogata and Matteo Lostaglio for valuable discussions. TS is supported by JSPS KAKENHI Grant Number JP16H02211 and JP19H05796. PhF is supported by the Institute for Quantum Information and Matter (IQIM) at Caltech which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907), from the Department of Energy Award de-sc0018407, and acknowledges contributions from the Swiss National Science Foundation (SNSF) via the NCCR QSIT as well as project No. 200020_165843. KK is supported by the Institute for Quantum Information and Matter (IQIM) at Caltech which is a National Science Foundation (NSF) Physics Frontiers Center (NSF Grant PHY-1733907). FB is is supported by the NSF.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Japan Society for the Promotion of Science (JSPS)JP16H02211
Japan Society for the Promotion of Science (JSPS)JP19H05796
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1733907
Department of Energy (DOE)DE-SC0018407
Swiss National Science Foundation (SNSF)200020_165843
Record Number:CaltechAUTHORS:20190801-134551728
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190801-134551728
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97604
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Aug 2019 21:32
Last Modified:04 Jun 2020 10:14

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