Continuity of the von Neumann entropy

Details Continuity of the von Neumann entropy Continuity of the von Neumann entropy

2009-04-13

arxiv.org/abs/0904.1963v3

Commun. Math. Phys., vol. 296, no. 3, 625-654 (2010).

Physics

Mathematical Physics

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

Scientific paper

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.

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