Criteria for equality in two entropic inequalities
Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 1045-1068
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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.
@article{SM_2014_205_7_a6,
author = {M. E. Shirokov},
title = {Criteria for equality in two entropic inequalities},
journal = {Sbornik. Mathematics},
pages = {1045--1068},
publisher = {mathdoc},
volume = {205},
number = {7},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2014_205_7_a6/}
}
M. E. Shirokov. Criteria for equality in two entropic inequalities. Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 1045-1068. http://geodesic.mathdoc.fr/item/SM_2014_205_7_a6/