Criteria for equality in two entropic inequalities

M. E. Shirokov

Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 1045-1068

Résumé

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.

Détail

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

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