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

Abstract

We describe the class (semigroup) of quantum channels mapping states with finite entropy into states with finite entropy. We show, in particular, that this class is naturally decomposed into three convex subclasses, two of them are closed under concatenations and tensor products. We obtain asymptotically tight universal continuity bounds for the output entropy of two types of quantum channels: channels with finite output entropy and energy-constrained channels preserving finiteness of the entropy.

21 pages, preliminary version, any comments are welcome. arXiv admin note: substantial text overlap with arXiv:1704.01905, arXiv:1907.02458

References in corpus (2)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• On Weyl channels being covariant with respect to the maximum commutative group of unitaries

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• Lower semicontinuity of the relative entropy disturbance and its corollaries
• New monotonicity property of the quantum relative entropy