One-dimensional discrete-time quantum walks on random environments

TL;DR

This paper studies one-dimensional quantum walks in random environments, providing mathematical theorems that describe their long-term behavior under different probabilistic conditions.

Contribution

It introduces a path counting method to establish weak limit theorems for quantum walks in random environments, covering both quenched and annealed cases.

Findings

Established weak limit theorems for quantum walks in random environments

Developed a path counting approach for analysis

Provided results for both quenched and annealed scenarios

Abstract

We consider discrete-time nearest-neighbor quantum walks on random environments in one dimension. Using the method based on a path counting, we present both quenched and annealed weak limit theorems for the quantum walk.