Central limit theorem for reducible and irreducible open quantum walks

TL;DR

This paper establishes central limit theorems for open quantum walks on multi-class networks, considering both regular and random class distributions, with implications for quantum biology and computation.

Contribution

It proves new central limit theorems for open quantum walks with multiple vertex classes and different distribution methods, expanding understanding of quantum stochastic processes.

Findings

Central limit theorems are proven for regular class distributions.

Central limit theorems are proven for random class distributions.

Numerical examples illustrate the theorems' applicability.

Abstract

In this work we aim at proving central limit theorems for open quantum walks on $\mathbb{Z}^d$. We study the case when there are various classes of vertices in the network. Furthermore, we investigate two ways of distributing the vertex classes in the network. First we assign the classes in a regular pattern. Secondly, we assign each vertex a random class with a uniform distribution. For each way of distributing vertex classes, we obtain an appropriate central limit theorem, illustrated by numerical examples. These theorems may have application in the study of complex systems in quantum biology and dissipative quantum computation.