Quantum conditional relative entropy and quasi-factorization of the relative entropy

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Standard

Quantum conditional relative entropy and quasi-factorization of the relative entropy. / Capel, Angela; Lucia, Angelo; Pérez-García, David.

I: Journal of Physics A: Mathematical and Theoretical, Bind 51, Nr. 48, 484001, 2018.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Capel, A, Lucia, A & Pérez-García, D 2018, 'Quantum conditional relative entropy and quasi-factorization of the relative entropy', Journal of Physics A: Mathematical and Theoretical, bind 51, nr. 48, 484001. https://doi.org/10.1088/1751-8121/aae4cf

APA

Capel, A., Lucia, A., & Pérez-García, D. (2018). Quantum conditional relative entropy and quasi-factorization of the relative entropy. Journal of Physics A: Mathematical and Theoretical, 51(48), [484001]. https://doi.org/10.1088/1751-8121/aae4cf

Vancouver

Capel A, Lucia A, Pérez-García D. Quantum conditional relative entropy and quasi-factorization of the relative entropy. Journal of Physics A: Mathematical and Theoretical. 2018;51(48). 484001. https://doi.org/10.1088/1751-8121/aae4cf

Author

Capel, Angela ; Lucia, Angelo ; Pérez-García, David. / Quantum conditional relative entropy and quasi-factorization of the relative entropy. I: Journal of Physics A: Mathematical and Theoretical. 2018 ; Bind 51, Nr. 48.

Bibtex

@article{17b2b02d615d488ebceac9f1a315db56,
title = "Quantum conditional relative entropy and quasi-factorization of the relative entropy",
abstract = "The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define the quantum conditional relative entropy and prove several quasi-factorization results for it. As an illustration of their potential, we use one of them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point.",
keywords = "conditional relative entropy, log-Sobolev inequality, mixing time, quantum dissipative evolution, quantum relative entropy, quasi-factorization of the relative entropy",
author = "Angela Capel and Angelo Lucia and David P{\'e}rez-Garc{\'i}a",
year = "2018",
doi = "10.1088/1751-8121/aae4cf",
language = "English",
volume = "51",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "Institute of Physics Publishing Ltd",
number = "48",

}

RIS

TY - JOUR

T1 - Quantum conditional relative entropy and quasi-factorization of the relative entropy

AU - Capel, Angela

AU - Lucia, Angelo

AU - Pérez-García, David

PY - 2018

Y1 - 2018

N2 - The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define the quantum conditional relative entropy and prove several quasi-factorization results for it. As an illustration of their potential, we use one of them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point.

AB - The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For that, we define the quantum conditional relative entropy and prove several quasi-factorization results for it. As an illustration of their potential, we use one of them to obtain a positive log-Sobolev constant for the heat-bath dynamics with product fixed point.

KW - conditional relative entropy

KW - log-Sobolev inequality

KW - mixing time

KW - quantum dissipative evolution

KW - quantum relative entropy

KW - quasi-factorization of the relative entropy

UR - http://www.scopus.com/inward/record.url?scp=85056477037&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aae4cf

DO - 10.1088/1751-8121/aae4cf

M3 - Journal article

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 48

M1 - 484001

ER -

ID: 198519028