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
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.
quantum state, quantum channel, von Neumann entropy, quantum mutual information, Holevo capacity of a quantum channel.
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Sbornik: Mathematics, 2014, 205:7, 1045–1068
MSC: Primary 81P45; Secondary 46N50
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
\paper Criteria for equality in two entropic inequalities
\jour Mat. Sb.
\jour Sb. Math.
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A. Jençová, “Preservation of a quantum Rényi relative entropy implies existence of a recovery map”, J. Phys. A, 50:8 (2017), 085303, 12 pp.
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