Around Shannon's Interpretation for Entropy-preserving Stochastic Averages

Understand

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.