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

201 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

Access to Document

10.1063/1.4838835

Cite this

@article{d1b5f0c486b94545b54f207f9098b146,

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.",

year = "2013",

month = dec,

day = "3",

doi = "10.1063/1.4838835",

language = "English (US)",

volume = "54",

journal = "Journal of Mathematical Physics",

issn = "0022-2488",

publisher = "American Institute of Physics",

number = "12",

}

TY - JOUR

T1 - Monotonicity of a relative Rényi entropy

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

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.

PY - 2013/12/3

Y1 - 2013/12/3

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].

UR - https://www.scopus.com/pages/publications/84891535488

UR - https://www.scopus.com/pages/publications/84891535488#tab=citedBy

U2 - 10.1063/1.4838835

DO - 10.1063/1.4838835

M3 - Article

AN - SCOPUS:84891535488

SN - 0022-2488

VL - 54

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 12

M1 - 122201

ER -

Monotonicity of a relative Rényi entropy

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this