Operational Entanglement of Symmetry-Protected Topological Edge States

TL;DR

This paper investigates the entanglement properties of symmetry-protected topological edge states in SSH ladders, revealing how topological phases enable non-bipartite many-body entanglement that can be experimentally accessed and transferred.

Contribution

It introduces an entanglement measure respecting particle number superselection and links topological edge states to operational entanglement, proposing an experimental protocol for Bell's inequality testing.

Findings

Topological phases with two filled edge states exhibit genuine many-body entanglement.

Entanglement can be extracted when edge states are localized on controlled sites.

Local particle number spectroscopy can detect entanglement onset.

Abstract

We use an entanglement measure that respects the superselection of particle number to study the non-local properties of symmetry-protected topological edge states. Considering half-filled M-leg Su-Schrieffer-Heeger (SSH) ladders as an example, we show that the topological properties and the operational entanglement extractable from the boundaries are intimately connected. Topological phases with at least two filled edge states have the potential to realize genuine, non-bipartite, many-body entanglement which can be transferred to a quantum register. The entanglement is extractable when the filled edge states are sufficiently localized on the lattice sites controlled by the users. We show, furthermore, that the onset of entanglement between the edges can be inferred from local particle number spectroscopy alone and present an experimental protocol to study the breaking of Bell's inequality.