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 such collision model with two bosonic ancillas entangled in a two-mode squeezed thermal state.

量子碰撞模型是一种有用的方法，可以通过系统与环境中某些粒子（通常称为“ancillas”）之间的重复相互作用来描述开放量子系统的动力学。在本文中，我们回顾了由多个子系统组成的多部分开放量子系统动力学的主要碰撞模型。特别是，我们对基于子系统和辅助系统之间基本碰撞的模型感兴趣，并在无穷小时间步长的限制下模拟全局和/或局部马尔可夫主方程。在讨论了基于通用碰撞的主方程推导的数学细节之后，我们在多部分系统碰撞模型的基础上提供了一般思想，我们讨论了它们的优点和局限性，我们展示了如何在量子计算机上模拟它们。此外，我们分析了基于纠缠附属物的碰撞模型的一些特性，推导出它为小时间步生成的主方程，并证明该主方程的系数受到限制其通用性的约束。最后，我们展示了这种碰撞模型的一个例子，其中两个玻色子辅助物纠缠在双模压缩热态中。