Entanglement Properties of Localized States in 1D Topological Quantum Walks

TL;DR

This paper investigates how localized states in 1D topological quantum walks relate to entanglement, showing that stronger localization correlates with lower entanglement, even under noise.

Contribution

It provides a detailed analysis of the entanglement properties of localized states in 1D topological quantum walks and their robustness to noise.

Findings

Localized states are associated with minima in entanglement.

Entanglement decreases with stronger localization.

Localized states persist under small bit-flip noise.

Abstract

The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with different topological numbers, can, for example, be effectively modelled using different coin parameters for the walk on either side of the interface. Depending on the neighbouring numbers, this can lead to localized states in one-dimensional configurations and here we carry out a detailed study into the strength of such localized states. We show that it can be related to the amount of entanglement created by the walks, with minima appearing for strong localizations. This feature also persists in the presence of small amounts of $\sigma_x$ (bit flip) noise.