Verifying multi-partite mode entanglement of W states

TL;DR

This paper presents a method to verify mode entanglement in N-mode W states, accounting for imperfections and distinguishing between different levels of multipartite entanglement, with practical implementation in optical systems.

Contribution

It introduces a novel verification technique for mode entanglement in W states that considers higher excitations and distinguishes entanglement levels, applicable with linear optics.

Findings

Method verifies mode entanglement with imperfections.

Distinguishes between full and partial N-party entanglement.

Applicable to optical systems with linear optics.

Abstract

We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M<N, including mixtures of the latter. We specialize to the case N=4 for illustrative purposes. In the optical case, where excitations are photons, our method can be implemented using linear optics.