Continuity of the von Neumann entropy

Abstract

A general method for proving continuity of the von Neumann entropy on subsets of positive trace-class operators is considered. This makes it possible to re-derive the known conditions for continuity of the entropy in more general forms and to obtain several new conditions. The method is based on a particular approximation of the von Neumann entropy by an increasing sequence of concave continuous unitary invariant functions defined using decompositions into finite rank operators. The existence of this approximation is a corollary of a general property of the set of quantum states as a convex topological space called the strong stability property. This is considered in the first part of the paper.

42 pages, the minor changes have been made, the new applications of the continuity condition have been added. To appear in Commun. Math. Phys

References in corpus (3)

• Entropic characteristics of subsets of states
• The Holevo capacity of infinite dimensional channels and the additivity problem
• Generalized compactness in linear spaces and its applications

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