How not to Rényi-generalize the quantum conditional mutual information

Paul Erker

doi:10.1088/1751-8113/48/27/275303

How not to Rényi-generalize the quantum conditional mutual information

Paul Erker

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.

Original language	English
Article number	275303
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	48
Issue number	27
DOIs	https://doi.org/10.1088/1751-8113/48/27/275303
Publication status	Published - 10 Jul 2015

Keywords

non-i.i.d.
quantum conditional mutual information
quantum information theory
Rényi divergences

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10.1088/1751-8113/48/27/275303

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title = "How not to R{\'e}nyi-generalize the quantum conditional mutual information",

abstract = "{\textcopyright} 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -R{\'e}nyi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -R{\'e}nyi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.",

keywords = "non-i.i.d., quantum conditional mutual information, quantum information theory, R{\'e}nyi divergences",

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N2 - © 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.

AB - © 2015 IOP Publishing Ltd. We study the relation between the quantum conditional mutual information and the quantum -Rényi divergences. Considering the totally antisymmetric state we show that it is not possible to attain a proper generalization of the quantum conditional mutual information by optimizing the distance in terms of quantum -Rényi divergences over the set of all Markov states. The failure of the approach considered arises from the observation that a small quantum conditional mutual information does not imply that the state is close to a quantum Markov state.

KW - non-i.i.d.

KW - quantum conditional mutual information

KW - quantum information theory

KW - Rényi divergences

U2 - 10.1088/1751-8113/48/27/275303

DO - 10.1088/1751-8113/48/27/275303

M3 - Article

VL - 48

IS - 27

M1 - 275303

ER -

How not to Rényi-generalize the quantum conditional mutual information

Abstract

Keywords

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