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.
Cite
@article{arxiv.0904.1963,
title = {Continuity of the von Neumann entropy},
author = {M. E. Shirokov},
journal= {arXiv preprint arXiv:0904.1963},
year = {2015}
}
Comments
42 pages, the minor changes have been made, the new applications of the continuity condition have been added. To appear in Commun. Math. Phys