Non Markovian Quantum Repeated Interactions and Measurements

TL;DR

This paper develops a non-Markovian quantum interaction model involving repeated system-environment interactions, deriving new master equations and measurement descriptions, and discusses unravelling in such systems.

Contribution

It introduces a novel non-Markovian framework for quantum repeated interactions, deriving discrete master equations and providing a rigorous measurement interpretation.

Findings

Derived discrete integro-differential and time-convolutionless master equations.

Provided a rigorous description of indirect quantum measurements in non-Markovian systems.

Discussed unravelling possibilities in non-Markovian quantum interaction models.

Abstract

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.