A brief journey through collision models for multipartite open quantum dynamics

TL;DR

This paper reviews collision models for multipartite open quantum systems, discussing their derivation, strengths, limitations, and simulation on quantum computers, with a focus on models involving entangled ancillas and their generated master equations.

Contribution

It provides a comprehensive overview of collision models for multipartite systems, including new insights into entangled ancilla models and their constraints.

Findings

Collision models can simulate global and local Markovian master equations.

Entangled ancilla collision models have constrained coefficients in their master equations.

Example provided with two bosonic ancillas in a two-mode squeezed thermal state.

Abstract

The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed "ancillas". In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal timestep. After discussing the mathematical details of the derivation of a generic collision-based master equation, we provide the general ideas at the basis of the collision models for multipartite systems, we discuss their strengths and limitations, and we show how they may be simulated on a quantum computer. Moreover, we analyze some properties of a collision model based on entangled ancillas, derive the master equation it generates for small timesteps, and prove that the coefficients of this master equation are subject to a constraint that limits their generality. Finally, we present an example of this collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.