Mappings preserving Segal’s entropy in von Neumann algebras. (English) Zbl 1430.46051
Summary: We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change the Segal entropy of the density of a normal, not necessarily normalised, state. Two cases are dealt with: a) no restriction on the map is imposed, b) the map represents a repeatable instrument in measurement theory which means that it is idempotent.
MSC:
| 46L57 | Derivations, dissipations and positive semigroups in \(C^*\)-algebras |
| 46L10 | General theory of von Neumann algebras |
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
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