Quantum central limit theorem for continuous-time quantum walks on odd graphs in quantum probability theory

TL;DR

This paper applies quantum probability theory to analyze the quantum central limit theorem for continuous-time quantum walks on odd graphs, providing a more straightforward approach to spectral analysis without heavy combinatorial methods.

Contribution

It introduces a novel quantum probability framework to study quantum walks on odd graphs, simplifying spectral analysis and proving a quantum central limit theorem.

Findings

Quantum probability theory effectively describes quantum walks on odd graphs.

The quantum central limit theorem holds for these walks under the new framework.

Simplifies spectral analysis compared to traditional combinatorial methods.

Abstract

The method of the quantum probability theory only requires simple structural data of graph and allows us to avoid a heavy combinational argument often necessary to obtain full description of spectrum of the adjacency matrix. In the present paper, by using the idea of calculation of the probability amplitudes for continuous-time quantum walk in terms of the quantum probability theory, we investigate quantum central limit theorem for continuous-time quantum walks on odd graphs.