Continuity of the von Neumann Entropy |
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Authors: | M E Shirokov |
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Institution: | (1) Naval Research Laboratory, Washington, DC, USA |
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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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Keywords: | |
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