The conditional entropy power inequality for quantum additive noise channels

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Standard

The conditional entropy power inequality for quantum additive noise channels. / De Palma, Giacomo; Huber, Stefan.

I: Journal of Mathematical Physics, Bind 59, Nr. 12, 122201, 2018, s. 1-20.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

De Palma, G & Huber, S 2018, 'The conditional entropy power inequality for quantum additive noise channels', Journal of Mathematical Physics, bind 59, nr. 12, 122201, s. 1-20. https://doi.org/10.1063/1.5027495

APA

De Palma, G., & Huber, S. (2018). The conditional entropy power inequality for quantum additive noise channels. Journal of Mathematical Physics, 59(12), 1-20. [122201]. https://doi.org/10.1063/1.5027495

Vancouver

De Palma G, Huber S. The conditional entropy power inequality for quantum additive noise channels. Journal of Mathematical Physics. 2018;59(12):1-20. 122201. https://doi.org/10.1063/1.5027495

Author

De Palma, Giacomo ; Huber, Stefan. / The conditional entropy power inequality for quantum additive noise channels. I: Journal of Mathematical Physics. 2018 ; Bind 59, Nr. 12. s. 1-20.

Bibtex

@article{d5515d2ef4b24a04a74d777e595dfa96,
title = "The conditional entropy power inequality for quantum additive noise channels",
abstract = "We prove the quantum conditional entropy power inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional entropy power inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional entropy power inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogs of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on entropy power inequalities.",
author = "{De Palma}, Giacomo and Stefan Huber",
year = "2018",
doi = "10.1063/1.5027495",
language = "English",
volume = "59",
pages = "1--20",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "12",

}

RIS

TY - JOUR

T1 - The conditional entropy power inequality for quantum additive noise channels

AU - De Palma, Giacomo

AU - Huber, Stefan

PY - 2018

Y1 - 2018

N2 - We prove the quantum conditional entropy power inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional entropy power inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional entropy power inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogs of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on entropy power inequalities.

AB - We prove the quantum conditional entropy power inequality for quantum additive noise channels. This inequality lower bounds the quantum conditional entropy of the output of an additive noise channel in terms of the quantum conditional entropies of the input state and the noise when they are conditionally independent given the memory. We also show that this conditional entropy power inequality is optimal in the sense that we can achieve equality asymptotically by choosing a suitable sequence of Gaussian input states. We apply the conditional entropy power inequality to find an array of information-theoretic inequalities for conditional entropies which are the analogs of inequalities which have already been established in the unconditioned setting. Furthermore, we give a simple proof of the convergence rate of the quantum Ornstein-Uhlenbeck semigroup based on entropy power inequalities.

UR - http://www.scopus.com/inward/record.url?scp=85058051131&partnerID=8YFLogxK

U2 - 10.1063/1.5027495

DO - 10.1063/1.5027495

M3 - Journal article

AN - SCOPUS:85058051131

VL - 59

SP - 1

EP - 20

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

M1 - 122201

ER -

ID: 211105776