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Andre Kornell (Mar 13 2024).

Abstract: We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. As an intermediate step, we prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if its adjusted Choi operator is a projection. Both equivalences generalize familiar facts about stochastic maps between finite sets.

Arxiv: https://arxiv.org/abs/2403.07229

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