Quantum walk on a ladder

TL;DR

This paper investigates quantum walks on a ladder structure using combined protocols, revealing how different boundary conditions and coin state differences influence probability distributions and information transfer.

Contribution

It introduces a novel approach to quantum walks on a ladder with mixed protocols, demonstrating control over probability distributions and mutual information transfer.

Findings

Three types of probability distributions can be achieved.

Maximum mutual information transfer occurs when coin state differences are maximized.

The walk's behavior depends on boundary conditions and coin state configurations.

Abstract

We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of these are the one-sided and alternative ones. Using the differences between coin states of the individual component, we can simulate the third case in which both components have identical probability profiles. We also observe that the mutual information transfer between two components of the walk is minimized when this difference across the two sides of the ladder is maximized.