Multipartite Correlations in Quantum Collision Models

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, and 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 the further analysis of memory effects in collisional quantum dynamics.

Automated summary

Researchers have developed a tensor network formalism to address the challenges in standard collision models, namely, describing quantum correlations among ancillas induced by successive system-ancilla interactions, and dealing with initially correlated ancillas. They found that matrix product state (matrix product density operator) is effective in capturing induced correlations in the standard collision model if the colliding particles are in pure (mixed) states. Additionally, they constructed a general tensor diagram for system dynamics and derived a memory-kernel master equation to handle initially correlated ancillas, considering multipoint correlations beyond two-point correlations.