Monotonicity of a relative Rényi entropy

Rupert L. Frank; Elliott H. Lieb

doi:10.1063/1.4838835

Monotonicity of a relative Rényi entropy

Rupert L. Frank, Elliott H. Lieb

Mathematics

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

141 Scopus citations

Abstract

We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al. ["On quantum Rényi entropies: A new definition, some properties," J. Math. Phys.54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].

Original language	English (US)
Article number	122201
Journal	Journal of Mathematical Physics
Volume	54
Issue number	12
DOIs	https://doi.org/10.1063/1.4838835
State	Published - Dec 3 2013

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.4838835

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title = "Monotonicity of a relative R{\'e}nyi entropy",

abstract = "We show that a recent definition of relative R{\'e}nyi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of M{\"u}ller-Lennert et al. [{"}On quantum R{\'e}nyi entropies: A new definition, some properties,{"} J. Math. Phys.54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].",

author = "Frank, {Rupert L.} and Lieb, {Elliott H.}",

note = "Funding Information: We thank E. Carlen, V. Jaksic, C.-A. Pillet, and A. Vershynina for valuable comments on a first draft of this paper. We are grateful to the referee for various suggestions that helped to improve this paper. U.S. National Science Foundation Grants Nos. PHY-1347399 (R.L.F.), PHY-0965859 and PHY-1265118 (E.H.L.), and the Simons Foundation Grant No. 230207 (E.H.L.) are acknowledged.",

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N1 - Funding Information: We thank E. Carlen, V. Jaksic, C.-A. Pillet, and A. Vershynina for valuable comments on a first draft of this paper. We are grateful to the referee for various suggestions that helped to improve this paper. U.S. National Science Foundation Grants Nos. PHY-1347399 (R.L.F.), PHY-0965859 and PHY-1265118 (E.H.L.), and the Simons Foundation Grant No. 230207 (E.H.L.) are acknowledged.

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N2 - We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al. ["On quantum Rényi entropies: A new definition, some properties," J. Math. Phys.54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].

AB - We show that a recent definition of relative Rényi entropy is monotone under completely positive, trace preserving maps. This proves a recent conjecture of Müller-Lennert et al. ["On quantum Rényi entropies: A new definition, some properties," J. Math. Phys.54, 122203 (2013); e-print arXiv:1306.3142v1; see also e-print arXiv:1306.3142].

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Monotonicity of a relative Rényi entropy

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