Multipartite correlations in quantum collision models

TL;DR

This paper introduces a tensor network formalism to describe quantum correlations in collision models, capturing both induced and initial correlations, and deriving a memory-kernel master equation to analyze higher-order multipoint correlations.

Contribution

It develops a tensor network approach for quantum collision models, addressing correlations among ancillas and deriving a master equation for complex memory effects.

Findings

Correlations are captured by matrix product states/density operators.

A general tensor diagram for system dynamics is constructed.

Higher-order multipoint correlations are analyzed in the memory kernel.

Abstract

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher order stroboscopic limits. These results open an avenue for a further analysis of memory effects in the collisional quantum dynamics.