Mappings preserving quantum Renyi's entropies in von Neumann algebras

TL;DR

This paper characterizes when certain trace-preserving maps on von Neumann algebras preserve quantum Renyi entropies, showing they must be Jordan *-isomorphisms to leave all entropies unchanged.

Contribution

It provides a complete characterization of entropy-preserving maps in the setting of semifinite von Neumann algebras, linking entropy invariance to Jordan *-isomorphisms.

Findings

Maps preserving a fixed quantum Renyi entropy are characterized

Such maps are Jordan *-isomorphisms if they preserve all entropies

The results connect entropy invariance with algebraic structure

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.