Quantum random walks and thermalisation

TL;DR

This paper develops a method to construct quantum random walks in arbitrary states and proves a convergence theorem demonstrating a thermalisation effect where the limiting dynamics follow a gauge-free quantum stochastic differential equation.

Contribution

It introduces a new construction for quantum random walks in any faithful normal state and establishes a convergence theorem showing thermalisation in the limit.

Findings

Quantum random walks can be constructed in arbitrary faithful normal states.

The convergence theorem demonstrates a thermalisation effect in the limit.

The limit cocycle satisfies a gauge-free quantum stochastic differential equation.

Abstract

It is shown how to construct quantum random walks with particles in an arbitrary faithful normal state. A convergence theorem is obtained for such walks, which demonstrates a thermalisation effect: the limit cocycle obeys a quantum stochastic differential equation without gauge terms. Examples are presented which generalise that of Attal and Joye (2007, J. Funct. Anal. 247, 253-288).