Unraveling open quantum systems: classical reductions and classical dilations of quantum markov semigroups

Abstract

A number of results connecting quantum and classical Markov semigroups, as well as their dilations is reported. The method presented here is based on the analysis of the structure of the semigroup generator. In particular, measure-valued processes appear as a combination of classical reduction and classical dilation of a given quantum Markov semigroup.