Time averaged distribution of a discrete-time quantum walk on the path

TL;DR

This paper studies the long-term behavior of discrete-time quantum walks on a path, deriving a weak limit theorem for their time-averaged distribution, which enhances understanding of quantum walk dynamics.

Contribution

It provides a new weak limit theorem for the time-averaged distribution of quantum walks on a path, connecting quantum walk behavior with classical random walk quantization.

Findings

Derived a weak limit theorem for the time-averaged distribution

Established the connection between quantum walks and classical random walks on a path

Enhanced understanding of quantum walk long-term behavior

Abstract

The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random walks on the path. We obtain a weak limit theorem for the time averaged distribution of our quantum walks.