A brief journey through collision models for multipartite open quantum dynamics

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.

Accepted version in the special issue of Open Syst. Inf. Dyn. devoted to the memory of Prof. A. Kossakowski. We have added the current Appendix A, new references, and additional discussions on the cascade master equation

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• Quantum non-stationary phenomena of spin systems in collision models
• Long-range interacting systems are locally non-interacting
• Experimental simulation of daemonic work extraction in open quantum batteries on a digital quantum computer
• Structured quantum collision models: generating coherence with thermal resources
• Simulating quantum transport via collisional models on a digital quantum computer
• Dissipative quantum many-body dynamics in (1+1)D quantum cellular automata and quantum neural networks
• Space-time correlations in monitored kinetically constrained discrete-time quantum dynamics
• Queued quantum collision models
• Non-linear classification capability of quantum neural networks due to emergent quantum metastability
• Continuous Variable Structured Collision Models
• Current circulation near additional energy degeneracy points in quadratic Fermionic networks
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Revealing emergent many-body phenomena by analyzing large-scale space-time records of monitored quantum systems