Limit theorems and absorption problems for quantum random walks in one dimension

TL;DR

This paper investigates limit theorems, symmetry, and absorption issues for two types of one-dimensional quantum random walks using the PQRS method, clarifying differences between the models introduced by Gudder and studied by Ambainis et al.

Contribution

It provides a unified analysis of two quantum walk models and clarifies their differences using the PQRS method.

Findings

Derived limit theorems for both walk types

Established symmetry properties of distributions

Analyzed absorption probabilities in quantum walks

Abstract

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by 2 times 2 unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.