Correlations break homogenization

TL;DR

This paper investigates how correlations among ancillas in a collisional model disrupt the homogenization process, using numerical and analytical methods with qubit and Gaussian models.

Contribution

It extends the homogenization paradigm to correlated ancillas and demonstrates that correlations can break the homogenization process.

Findings

Correlations among ancillas prevent the system from reaching the ancillas' state.

Numerical simulations with qubit models show disruption of homogenization.

Analytical results with Gaussian models confirm the impact of correlations.

Abstract

The standard collisional model paradigm consists of a system that interacts sequentially with identically prepared ancillas. After infinitely many collisions, and under appropriate conditions, the system may converge to the same state as the ancillas. This process, known as homogenization, is independent of the ancilla initial state, being a property only of the underlying dynamics. In this paper we extend this idea to locally identical, but globally correlated, ancillas, and show that correlations break homogenization. This is done numerically using a minimal qubit model, and analytically using an exactly soluble Gaussian model. In both cases, we use Hamiltonian graph states with cyclic graphs as the prototypical method for building scalable many-body entangled ancillary states.