Mappings preserving quantum Renyi's entropies in von Neumann algebras

• URL: http://arxiv.org/abs/2302.02282v1
• Date: Sun, 5 Feb 2023 02:41:39 GMT
• Title: Mappings preserving quantum Renyi's entropies in von Neumann algebras
• Authors: Andrzej {\L}uczak, Hanna Pods\k{e}dkowska, Rafa{\l} Wieczorek
• Abstract summary: A normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.

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