# A limit theorem for a splitting distribution of a quantum walk

## TL;DR

This paper establishes a limit theorem for a specific quantum walk that splits into two parts, analyzing the long-term probability distribution of the walker's position after many steps.

## Contribution

It introduces a new limit theorem for a quantum walk with a splitting distribution, providing insights into its asymptotic behavior.

## Key findings

- Derived the long-time limit distribution of the quantum walk
- Showed the probability distribution splits into two parts over time
- Provided an approximation to the walker's position probability after many steps

## Abstract

Discrete-time quantum walks are considered a counterpart of random walks and the study for them has been getting attention since around 2000. In this paper, we focus on a quantum walk which generates a probability distribution splitting to two parts. The quantum walker with two coin states spreads at points, represented by integers, and we analyze the chance of finding the walker at each position after it carries out a unitary evolution a lot of times. The result is reported as a long-time limit distribution from which one can see an approximation to the finding probability.