Entropy characteristics of subsets of states.~I

M. E. Shirokov

Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1265-1292.

Résumé

We study the properties of quantum entropy and $\chi$-capacity (regarded as a function of sets of quantum states) in the infinite-dimensional case. We obtain conditions for the boundedness and continuity of the restriction of the entropy to a subset of quantum states, as well as conditions for the existence of the state with maximal entropy in certain subsets. The notion of $\chi$-capacity is considered for an arbitrary subset of states. The existence of an optimal average is proved for an arbitrary subset with finite $\chi$-capacity. We obtain a sufficient condition for the existence of an optimal measure and prove a generalized maximal distance property.

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