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Izvestiya Mathematics

Entropy characteristics of subsets of states. II

Максим Евгеньевич Широков

Published Feb 28, 2007• 10 citations
Publisher

Abstract

We study the properties of quantum entropy and -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 -capacity is considered for an arbitrary subset of states. The existence of an optimal average is proved for an arbitrary subset with finite -capacity. We obtain a sufficient condition for the existence of an optimal measure and prove a generalized maximal distance property.

DOI
10.1070/im2007v071n01abeh002354

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