Master equations for correlated quantum channels

TL;DR

This paper derives a general master equation for multipartite quantum systems interacting with a large environment, capturing correlated Markovian dynamics and cross-system correlations without specific system-environment assumptions.

Contribution

It introduces a collisional model that produces a correlated Markovian master equation for multipartite quantum systems, including pairwise cross correlations.

Findings

The model yields a Lindblad super-operator with pairwise cross terms.

It applies to arbitrary multipartite systems and environments.

No specific assumptions on system or environment nature are required.

Abstract

We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem "collides" with the same sequence of sub-environments which, in between the collisions, evolve according to a map that mimics relaxations effects. No assumption is made on the specific nature of neither the system nor the environment. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Linblad super-operator contains pairwise terms describing cross correlation between the different subsystems.