Continuous-Time Quantum Walks on Trees in Quantum Probability Theory

TL;DR

This paper develops a quantum central limit theorem for continuous-time quantum walks on trees using quantum probability theory, revealing new limit theorems and showing the limit density resembles that of walks on a 1D lattice.

Contribution

It introduces a quantum central limit theorem for walks on trees and presents new limit theorems for a different continuous-time walk, expanding quantum walk theory.

Findings

Derived a quantum central limit theorem for walks on trees

Established new limit theorems for a different continuous-time walk

Found the limit density similar to that of walks on a 1D lattice

Abstract

A quantum central limit theorem for a continuous-time quantum walk on a homogeneous tree is derived from quantum probability theory. As a consequence, a new type of limit theorems for another continuous-time walk introduced by the walk is presented. The limit density is similar to that given by a continuous-time quantum walk on the one-dimensional lattice.