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Continuity of the von Neumann Entropy

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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.

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  1. Steklov Mathematical Institute, Gubkina Str. 8, 11991, Moscow, Russia

    M. E. Shirokov

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  1. M. E. Shirokov
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Communicated by M.B. Ruskai

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Shirokov, M.E. Continuity of the von Neumann Entropy. Commun. Math. Phys. 296, 625–654 (2010). https://doi.org/10.1007/s00220-010-1007-x

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  • DOI: https://doi.org/10.1007/s00220-010-1007-x

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