Quantum homogenization in non-Markovian collisional model

TL;DR

This paper investigates quantum homogenization in a non-Markovian collisional model with bath-bath interactions, demonstrating that homogenization occurs but at a slower rate, and exploring how different bath unitaries affect the process.

Contribution

It introduces a non-Markovian collisional model with bath-bath interactions and analyzes how different unitaries influence quantum homogenization.

Findings

Homogenization occurs regardless of initial states.

Slower homogenization rate compared to Markovian case.

Bath-bath unitaries can speed up homogenization but reduce universality.

Abstract

Collisional models are a category of microscopic framework designed to study open quantum systems. The framework involves a system sequentially interacting with a bath comprised of identically prepared units. In this regard, quantum homogenization is a process where the system state approaches the identically prepared state of bath unit in the asymptotic limit. Here, we study the homogenization process for a single qubit in the non-Markovian collisional model framework generated via additional bath-bath interaction. With partial swap operation as both system-bath and bath-bath unitary, we numerically demonstrate that homogenization is achieved irrespective of the initial states of the system or bath units. This is reminiscent of the Markovian scenario, where partial swap is the unique operation for a universal quantum homogenizer. On the other hand, we observe that the rate of homogenization is slower than its Markovian counter part. Interestingly, a different choice of bath-bath unitary speeds up the homogenization process but loses the universality, being dependent on the initial states of the bath units.