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arXiv · 2403.07229

Characterizations of homomorphisms among unital completely positive maps

Andre Kornell
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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. This adjusted von Neumann entropy is the negative of the relative entropy with respect to the uniform state on the C*-algebra, up to an additive constant. 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.

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Andre Kornell. 2024-03-12. Characterizations of homomorphisms among unital completely positive maps. https://arxiv.org/abs/2403.07229

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