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Title: Criteria for equality in two entropic inequalities

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. (paper)

Authors:
 [1]
  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow (Russian Federation)
Publication Date:
OSTI Identifier:
22364928
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 7; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; BOSONS; DEPOLARIZATION; ENTROPY; KERNELS; MAPS; MIXED STATE; MIXED STATES; QUANTUM INFORMATION

Citation Formats

Shirokov, M. E., E-mail: msh@mi.ras.ru. Criteria for equality in two entropic inequalities. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N07ABEH004409.
Shirokov, M. E., E-mail: msh@mi.ras.ru. Criteria for equality in two entropic inequalities. United States. doi:10.1070/SM2014V205N07ABEH004409.
Shirokov, M. E., E-mail: msh@mi.ras.ru. Thu . "Criteria for equality in two entropic inequalities". United States. doi:10.1070/SM2014V205N07ABEH004409.
@article{osti_22364928,
title = {Criteria for equality in two entropic inequalities},
author = {Shirokov, M. E., E-mail: msh@mi.ras.ru},
abstractNote = {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. (paper)},
doi = {10.1070/SM2014V205N07ABEH004409},
journal = {Sbornik. Mathematics},
number = 7,
volume = 205,
place = {United States},
year = {Thu Jul 31 00:00:00 EDT 2014},
month = {Thu Jul 31 00:00:00 EDT 2014}
}