# Proving genuine multiparticle entanglement from separable nearest-neighbor marginals

## TL;DR

This paper investigates whether global multiparticle entanglement can be inferred solely from local, separable two-body marginals, demonstrating methods to identify such states up to six particles and extending to larger systems.

## Contribution

It introduces an iterative semidefinite programming approach to prove the existence of genuinely multiparticle entangled states with separable marginals, and provides a construction method for larger systems.

## Key findings

- Existence of multiparticle entangled states with separable marginals up to six particles
- Method to construct such states for larger systems and higher dimensions
- Use of semidefinite programs to verify entanglement properties

## Abstract

We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable, but where the entanglement can be proven using knowledge of a subset of the marginals only. Using an iteration of semidefinite programs we prove that for any possible marginal configuration up to six particles multiqubit states with the desired properties can be found. We then present a method to construct states with the same properties for more particles in higher dimensions.