Publications of the Research Institute for Mathematical Sciences· 2026Q2
Mappings Preserving Quantum Rényi’s Entropies in Von Neumann Algebras
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- Q2SCImago
- 2026year
Short summary
A trace-preserving unital map on a semifinite von Neumann algebra preserves fixed quantum Rényi entropy if and only if it is a Jordan *-isomorphism.
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Key points
- Investigates trace-preserving unital maps on semifinite von Neumann algebras.
- Identifies condition for these maps to preserve fixed quantum Rényi entropy.
- Proves that entropy preservation is equivalent to the map being a Jordan *-isomorphism.
AI-generated from the title and abstract; the full text is not read.
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 Rényi 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.
The authors' abstract, as published at the source. Publications of the Research Institute for Mathematical Sciences, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics