Relative entropy convergence for depolarizing channels

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Standard

Relative entropy convergence for depolarizing channels. / Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.

In: Journal of Mathematical Physics, Vol. 57, No. 2, 022202, 02.2016.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Müller-Hermes, A, Stilck França, D & Wolf, MM 2016, 'Relative entropy convergence for depolarizing channels', Journal of Mathematical Physics, vol. 57, no. 2, 022202. https://doi.org/10.1063/1.4939560

APA

Müller-Hermes, A., Stilck França, D., & Wolf, M. M. (2016). Relative entropy convergence for depolarizing channels. Journal of Mathematical Physics, 57(2), [022202]. https://doi.org/10.1063/1.4939560

Vancouver

Müller-Hermes A, Stilck França D, Wolf MM. Relative entropy convergence for depolarizing channels. Journal of Mathematical Physics. 2016 Feb;57(2). 022202. https://doi.org/10.1063/1.4939560

Author

Müller-Hermes, Alexander ; Stilck França, Daniel ; Wolf, Michael M. / Relative entropy convergence for depolarizing channels. In: Journal of Mathematical Physics. 2016 ; Vol. 57, No. 2.

Bibtex

@article{47cfb617fde7436d99450fe4862d30fa,
title = "Relative entropy convergence for depolarizing channels",
abstract = "We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application, we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von Neumann entropy. This result is compared to similar bounds obtained recently by Kim and we show a version of Pinsker{\textquoteright}s inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer{\textquoteright}s inequality to prove a uniform lower bound",
author = "Alexander M{\"u}ller-Hermes and {Stilck Fran{\c c}a}, Daniel and Wolf, {Michael M.}",
year = "2016",
month = feb,
doi = "10.1063/1.4939560",
language = "English",
volume = "57",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "2",

}

RIS

TY - JOUR

T1 - Relative entropy convergence for depolarizing channels

AU - Müller-Hermes, Alexander

AU - Stilck França, Daniel

AU - Wolf, Michael M.

PY - 2016/2

Y1 - 2016/2

N2 - We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application, we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von Neumann entropy. This result is compared to similar bounds obtained recently by Kim and we show a version of Pinsker’s inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer’s inequality to prove a uniform lower bound

AB - We study the convergence of states under continuous-time depolarizing channels with full rank fixed points in terms of the relative entropy. The optimal exponent of an upper bound on the relative entropy in this case is given by the log-Sobolev-1 constant. Our main result is the computation of this constant. As an application, we use the log-Sobolev-1 constant of the depolarizing channels to improve the concavity inequality of the von Neumann entropy. This result is compared to similar bounds obtained recently by Kim and we show a version of Pinsker’s inequality, which is optimal and tight if we fix the second argument of the relative entropy. Finally, we consider the log-Sobolev-1 constant of tensor-powers of the completely depolarizing channel and use a quantum version of Shearer’s inequality to prove a uniform lower bound

U2 - 10.1063/1.4939560

DO - 10.1063/1.4939560

M3 - Journal article

VL - 57

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 2

M1 - 022202

ER -

ID: 168886587