Continuous-Time Quantum Walk on Locally Infinite Graph

TL;DR

This paper introduces a continuous-time quantum walk model on a locally infinite graph and reveals that its time-reversal symmetry can be described by a unitary operator, contrasting with classical anti-unitary descriptions.

Contribution

The study presents a novel quantum walk model on a specific graph and demonstrates that its time-reversal symmetry is represented by a unitary operator, unlike classical cases.

Findings

Time-reversal symmetry in the model is described by a unitary operator.

Spectral properties of the quantum walk are analyzed.

Contrasts with classical time-reversal symmetry are established.

Abstract

Time-reversal symmetry is of fundamental importance to physics. In the classical theory of time-reversal symmetry, the time-reversal symmetry of a quantum system is described by an anti-unitary operator, which is known as the time-reversal operator of the system. In this paper, we introduce and study a model of continuous-time quantum walk on a special locally infinite graph. After examining its spectral property, we investigate the time-reversal symmetry of the model. To our surprise, we find that its time-reversal symmetry can be described directly by a unitary operator, which contrasts sharply with that in the classical theory of time-reversal symmetry. Some other related results are also proven.