Markovian embedding of non-Markovian quantum collisional models

TL;DR

This paper shows how non-Markovian quantum collisional models can be embedded into bipartite Markovian Lindblad dynamics, linking phenomenological models with measurement theory and demonstrating non-Markovian effects like information backflow.

Contribution

It introduces a method to embed non-Markovian quantum collisional models into bipartite Markovian Lindblad dynamics using continuous monitoring of an auxiliary system.

Findings

Models reproduce non-Markovian effects such as information backflow.

The approach connects phenomenological models with measurement-based quantum dynamics.

Demonstrates the embedding of non-Markovian dynamics into Markovian frameworks.

Abstract

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of stochastic realizations that consist in the application at random times of a (collisional) completely positive transformation over the system state. In this paper, we demonstrate that these kinds of models can be embedded in bipartite Markovian Lindblad dynamics consisting of the system of interest and an auxiliary one. In contrast with phenomenological formulations, here the stochastic ensemble dynamics an the inter-event time interval statistics are obtained from a quantum measurement theory after assuming that the auxiliary system is continuously monitored in time. Models where the system inter-collisional dynamics is non-Markovian [B. Vacchini, Phys. Rev. A 87, 030101(R) (2013)] are also obtained from the present approach. The formalism is exemplified through bipartite dynamics that leads to non-Markovian system effects such as an environment-to-system back flow of information.