Quantum random walk approximation on locally compact quantum groups

TL;DR

This paper develops a scheme to approximate quantum Levy processes on locally compact quantum groups using quantum random walks, extending to broader discrete approximations of quantum stochastic processes on C*-bialgebras.

Contribution

It introduces a natural approximation scheme for quantum Levy processes on quantum groups via quantum random walks, broadening the context to include quantum stochastic convolution cocycles.

Findings

Established a scheme for approximation of quantum Levy processes

Extended the framework to discrete approximations of quantum stochastic cocycles

Applicable to locally compact quantum groups and C*-bialgebras

Abstract

A natural scheme is established for the approximation of quantum Levy processes on locally compact quantum groups by quantum random walks. We work in the somewhat broader context of discrete approximations of completely positive quantum stochastic convolution cocycles on C*-bialgebras.