Characterizations of homomorphisms among unital completely positive maps
- URL: http://arxiv.org/abs/2403.07229v1
- Date: Tue, 12 Mar 2024 00:55:44 GMT
- Title: Characterizations of homomorphisms among unital completely positive maps
- Authors: Andre Kornell
- Abstract summary: 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 maps between finite sets.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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