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Mat. Sb., 2014, Volume 205, Number 7, Pages 135–160 (Mi msb8288)  

This article is cited in 1 scientific paper (total in 1 paper)

Criteria for equality in two entropic inequalities

M. E. Shirokov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: We obtain a simple criterion for local equality between the constrained Holevo capacity and the quantum mutual information of a quantum channel. This shows that the set of all states for which this equality holds is determined by the kernel of the channel (as a linear map).
Applications to Bosonic Gaussian channels are considered. It is shown that for a Gaussian channel having no completely depolarizing components the above characteristics may coincide only at non-Gaussian mixed states and a criterion for the existence of such states is given.
All the obtained results may be reformulated as conditions for equality between the constrained Holevo capacity of a quantum channel and the input von Neumann entropy.
Bibliography: 20 titles.

Keywords: quantum state, quantum channel, von Neumann entropy, quantum mutual information, Holevo capacity of a quantum channel.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 12-01-00319-а
13-01-00295-a


DOI: https://doi.org/10.4213/sm8288

Full text: PDF file (693 kB)
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English version:
Sbornik: Mathematics, 2014, 205:7, 1045–1068

Bibliographic databases:

UDC: 519.248.3
MSC: Primary 81P45; Secondary 46N50
Received: 07.10.2013

Citation: M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Mat. Sb., 205:7 (2014), 135–160; Sb. Math., 205:7 (2014), 1045–1068

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. Jençová, “Preservation of a quantum Rényi relative entropy implies existence of a recovery map”, J. Phys. A, 50:8 (2017), 085303, 12 pp.  crossref  mathscinet  zmath  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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