Quasi-stationary normal states for quantum Markov semigroups

TL;DR

This paper introduces Quasi-Stationary States (QSS) for quantum Markov semigroups, linking them to spectral properties and measurement theory, with illustrative examples demonstrating their features.

Contribution

It generalizes classical quasi-stationary distributions to quantum Markov semigroups and connects QSSs to spectral analysis and measurement interpretations.

Findings

QSSs generalize classical quasi-stationary distributions.

Connection established between QSSs and spectral properties.

Examples illustrate interesting features of QSSs.

Abstract

We introduce the notion of Quasi-Stationary State (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation of QSSs using the theory of direct and indirect quantum measurements. Moreover, we prove that there is a connection between QSSs and spectral properties of the quantum Markov semigroup. Finally, we discuss some examples which, despite their simplicity, already show interesting features.