Non-Markovianity in collision models with initial intra-environment correlations

TL;DR

This paper explores how initial entanglement between environment components in collision models influences the non-Markovian behavior of an open quantum system, revealing that pre-existing ancilla entanglement induces non-Markovian dynamics.

Contribution

It introduces a framework to map correlated collision models onto an enlarged Markovian system and demonstrates how initial ancilla entanglement controls non-Markovianity.

Findings

Ancilla-ancilla entanglement prior to system collision induces non-Markovian dynamics.

System-ancilla entanglement before ancilla-ancilla entanglement results in Markovian behavior.

Correlations within the environment significantly influence the system's memory effects.

Abstract

Collision models (CMs) describe an open system interacting in sequence with elements of an environment, termed ancillas. They have been established as a useful tool for analyzing non-Markovian open quantum dynamics based on the ability to control the environmental memory through simple feedback mechanisms. In this work, we investigate how ancilla-ancilla entanglement can serve as a mechanism for controlling the non-Markovianity of an open system, focusing on an operational approach to generating correlations within the environment. To this end, we first demonstrate that the open dynamics of CMs with sequentially generated correlations between groups of ancillas can be mapped onto a composite CM, where the memory part of the environment is incorporated into an enlarged Markovian system. We then apply this framework to an all-qubit CM, and show that non-Markovian behavior emerges only when the next incoming pair of ancillas are entangled prior to colliding with the system. On the other hand, when system-ancilla collisions precede ancilla-ancilla entanglement, we find the open dynamics to always be Markovian. Our findings highlight how certain qualitative features of inter-ancilla correlations can strongly influence the onset of system non-Markovianity.