Entropy production of doubly stochastic quantum channels

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Standard

Entropy production of doubly stochastic quantum channels. / Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.

I: Journal of Mathematical Physics, Bind 57, Nr. 2, 022203, 01.02.2016.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Müller-Hermes, A, Stilck França, D & Wolf, MM 2016, 'Entropy production of doubly stochastic quantum channels', Journal of Mathematical Physics, bind 57, nr. 2, 022203. https://doi.org/10.1063/1.4941136

APA

Müller-Hermes, A., Stilck França, D., & Wolf, M. M. (2016). Entropy production of doubly stochastic quantum channels. Journal of Mathematical Physics, 57(2), [022203]. https://doi.org/10.1063/1.4941136

Vancouver

Müller-Hermes A, Stilck França D, Wolf MM. Entropy production of doubly stochastic quantum channels. Journal of Mathematical Physics. 2016 feb. 1;57(2). 022203. https://doi.org/10.1063/1.4941136

Author

Müller-Hermes, Alexander ; Stilck França, Daniel ; Wolf, Michael M. / Entropy production of doubly stochastic quantum channels. I: Journal of Mathematical Physics. 2016 ; Bind 57, Nr. 2.

Bibtex

@article{5c58ac3a26da4854a5611da862216655,
title = "Entropy production of doubly stochastic quantum channels",
abstract = "We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.",
author = "Alexander M{\"u}ller-Hermes and {Stilck Fran{\c c}a}, Daniel and Wolf, {Michael M.}",
year = "2016",
month = feb,
day = "1",
doi = "10.1063/1.4941136",
language = "English",
volume = "57",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "2",

}

RIS

TY - JOUR

T1 - Entropy production of doubly stochastic quantum channels

AU - Müller-Hermes, Alexander

AU - Stilck França, Daniel

AU - Wolf, Michael M.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

AB - We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

U2 - 10.1063/1.4941136

DO - 10.1063/1.4941136

M3 - Journal article

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 022203

ER -

ID: 232254551