Spatial entanglement between two quantum walkers with exchange symmetric coins

TL;DR

This paper explores how initial and final exchange symmetries influence the spatial entanglement dynamics in two-coin quantum walks, revealing symmetry-dependent transfer and oscillation behaviors with implications for quantum technology.

Contribution

It demonstrates the impact of exchange symmetries on entanglement transfer and oscillation patterns in quantum walks, a novel insight into symmetry effects on quantum entanglement dynamics.

Findings

Initial anti-symmetric states transfer entanglement to position space under symmetric measurements.

Anti-symmetric final outcomes cause damped oscillations in spatial entanglement.

Symmetry-lacking post-selected results lead to consistent entanglement damping.

Abstract

We investigate how the initial and final exchange symmetries between the two-coin states influence the spatial entanglement dynamics between the two corresponding quantum walkers. Notably, when the initial state is anti-symmetric and the final measurement on the coins yields symmetric outcomes, all the initial entanglement will be transferred to the spatial degrees of freedom, regardless of when the coins are measured. Conversely, if the final outcomes are anti-symmetric, the spatial entanglement exhibits damped oscillation with a period ($T$) being inversely proportional to the coin operator parameter ($\theta$). These behaviours are reversed for symmetric initial states. Moreover, we also observe the same spatial entanglement damping regardless of the initial state when the post-selected results lack symmetry. Our findings reveal how symmetries affect the entanglement dynamics in quantum walks, offering potential insights for applications in quantum technology.