Mediated Homogenization

TL;DR

This paper investigates quantum homogenization protocols, introducing mediated schemes with networks of qudits, analyzing entanglement effects, and proving convergence to equilibrium in Heisenberg chains.

Contribution

It presents a formalism for analyzing mediated homogenization, explores entanglement in network configurations, and proves convergence in complex quantum systems.

Findings

Mediated homogenization schemes can relax to fixed states via partial bath interactions.

Entanglement can be introduced among network elements during homogenization.

Convergence to equilibrium is proven for Heisenberg chains with competing baths.

Abstract

Homogenization protocols model the quantum mechanical evolution of a system to a fixed state independently from its initial configuration by repeatedly coupling it with a collection of identical ancillas. Here we analyze these protocols within the formalism of "relaxing" channels providing an easy to check sufficient condition for homogenization. In this context we describe mediated homogenization schemes where a network of connected qudits relaxes to a fixed state by only partially interacting with a bath. We also study configurations which allow us to introduce entanglement among the elements of the network. Finally we analyze the effect of having competitive configurations with two different baths and we prove the convergence to dynamical equilibrium for Heisenberg chains.