Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins

TL;DR

This paper analyzes the long-term behavior of three-state quantum walks on a line with generalized Grover coins, proving limit theorems and demonstrating localization effects influenced by coin parameters.

Contribution

It provides new limit theorems for three-state quantum walks and explores how coin parameters affect localization and peak velocities.

Findings

Quantum walks exhibit localization at initial position.

Limit theorems describe asymptotic behavior.

Coin parameters influence peak velocities.

Abstract

In this article, we undertake a detailed study of the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. Two limit theorems are proved and consequently we show that the quantum walk exhibits localization at its initial position, for a wide range of coin parameters. Finally, we discuss the effect of the coin parameters on the peak velocities of probability distributions of the underlying quantum walks.