Simple characterization of positive linear maps preserving continuity of the von Neumann entropy

Abstract

We show that a positive linear map preserves local continuity (convergence) of the entropy if and only if it preserves finiteness of the entropy, i.e. transforms operators with finite entropy to operators with finite entropy. The last property is equivalent to the boundedness of the output entropy of a map on the set of pure states.

8 pages, the second part of v1 is moved to arXiv:2004.03582

References in corpus (1)

• Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints

Cited by in corpus (1)

• On quantum channels and operations preserving finiteness of the von Neumann entropy