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

• URL: http://arxiv.org/abs/2204.05625v2
• Date: Tue, 13 Sep 2022 05:08:06 GMT
• Title: Limit theorems and localization of three state quantum walks on a line defined by generalized Grover coins
• Authors: Amrita Mandal, Rohit Sarma Sarkar, Shantanav Chakraborty, Bibhas Adhikari
• Abstract summary: We study the limiting behavior of a three-state discrete-time quantum walk on one dimensional lattice with generalized Grover coins. We show that the quantum walk exhibits localization at its initial position, for a wide range of coin parameters.
• Score: 0.15749416770494704
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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