Two quantum walkers sharing coins

TL;DR

This paper investigates how partial or full swapping of coins affects two independent quantum walks, revealing complex quantum correlations and features absent in classical random walks.

Contribution

It introduces a novel analysis of inter-walker quantum correlations in quantum walks with coin swapping, highlighting unique quantum features.

Findings

Quantum walks with coin swapping exhibit complex inter-walker correlations.

Quantum correlations are present without classical analogues.

Swapping coins significantly influences quantum walk behavior.

Abstract

We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk characteristics, but we show that quantum walks with partial swapping of coins have complicated yet elegant inter-walker correlations. Specifically we study the joint position distribution of the reduced two-walker state after tracing out the coins and analyze total, classical and quantum correlations in terms of the mutual information, the quantum mutual information, and the measurement-induced disturbance. Our analysis shows intriguing quantum features without classical analogues.