Quantum random walks and their convergence

TL;DR

This paper establishes the strong convergence of quantum random walks with bounded structure maps, extending previous results to infinite-dimensional noise using coordinate-free quantum stochastic calculus.

Contribution

It introduces a coordinate-free approach to quantum random walks and proves their strong convergence in the infinite-dimensional noise setting.

Findings

Proved strong convergence of quantum random walks with bounded structure maps.

Extended convergence results from one-dimensional to infinite-dimensional noise.

Utilized coordinate-free quantum stochastic calculus for the analysis.

Abstract

Using coordinate-free basic operators on toy Fock spaces \cite{AP}, quantum random walks are defined following the ideas in \cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under suitable assumptions, extendings the result obtained in \cite{KBS} in case of one dimensional noise. To handle infinite dimensional noise we have used the coordinate-free language of quantum stochastic calculus developed in \cite{GS1}.