Christensen-Evans theorem and extensions of GNS-symmetric quantum Markov semigroups

TL;DR

This paper refines the Christensen-Evans theorem for GNS-symmetric quantum Markov semigroups, demonstrating the existence of symmetric extensions and characterizing generators on finite-dimensional algebras.

Contribution

It provides a refined version of the Christensen-Evans theorem and establishes the existence of GNS-symmetric extensions for quantum Markov semigroups.

Findings

Refined Christensen-Evans theorem for GNS-symmetric semigroups

Existence of GNS-symmetric extensions proven

Generators on finite-dimensional algebras characterized by Alicki's form

Abstract

In this note we prove a refined version of the Christensen-Evans theorem for generators of uniformly continuous GNS-symmetric quantum Markov semigroups. We use this result to show the existence of GNS-symmetric extensions of GNS-symmetric quantum Markov semigroups. In particular, this implies that the generators of GNS-symmetric quantum Markov semigroups on finite-dimensional von Neumann algebra can be written in the form specified by Alicki's theorem.