Around Shannon's Interpretation for Entropy-preserving Stochastic Averages

TL;DR

This paper characterizes when positive unital trace-preserving maps on matrix algebras preserve von Neumann entropy, showing they act as *-automorphisms and relate to zero-entropy stochastic matrices.

Contribution

It provides new characterizations of entropy-preserving maps, linking algebraic automorphisms with entropy conditions in quantum information theory.

Findings

Maps preserving von Neumann entropy are *-automorphisms.

Entropy preservation is equivalent to zero entropy in associated stochastic matrices.

Provides criteria for entropy-preserving transformations in quantum systems.

Abstract

We give various characterizations for a positive unital Tr-preserving map on a matrix algebra to preserve the von Neumann entropy of a state. Among others, it is given by that the map behaves as a *-automorphism. This is also equivalent to that the entropy of the stochastic matrix arising from the map and the state is zero.