Around Shannon's interpretation for entropy-preserving stochastic averages

摘要

Let Phi be a positive unital Tr-preserving map on M-n(C). We give various characterizations for Phi to preserve the von Neumann entropy of a state rho on M-n(C). Among others, it is given by that Phi behaves to rho as a *-automorphism. This is also equivalent to that the entropy of the stochastic matrix arising from {rho, Phi} is zero.