Directional correlations in quantum walks with two particles

TL;DR

This paper investigates directional correlations in two-particle quantum walks on a line, deriving asymptotic expressions for non-interacting particles and showing how interactions can enhance correlations beyond non-interacting limits.

Contribution

It provides analytical results for two-particle quantum walks, including the effects of interactions, advancing understanding of collective quantum effects in such systems.

Findings

Analytic asymptotic expressions for non-interacting particles

Limits of directional correlations identified

Interaction can surpass non-interacting correlation limits

Abstract

Quantum walks on the line with a single particle possess a classical analog. Involving more walkers opens up the possibility to study collective quantum effects, such as many particle correlations. In this context, entangled initial states and indistinguishability of the particles play a role. We consider directional correlations between two particles performing a quantum walk on a line. For non-interacting particles we find analytic asymptotic expressions and give the limits of directional correlations. We show that introducing $\delta$-interaction between the particles, one can exceed the limits for non-interacting particles.