Geodesic
Entropy characteristics of subsets of states.~I
Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1265-1292

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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. 
@article{IM2_2006_70_6_a7,
     author = {M. E. Shirokov},
     title = {Entropy characteristics of subsets of {states.~I}},
     journal = {Izvestiya. Mathematics },
     pages = {1265--1292},
     publisher = {mathdoc},
     volume = {70},
     number = {6},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2006_70_6_a7/}
}
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M. E. Shirokov. Entropy characteristics of subsets of states.~I. Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1265-1292. http://geodesic.mathdoc.fr/item/IM2_2006_70_6_a7/