Convicting emergent multipartite entanglement with evidence from a partially blind witness

TL;DR

This paper demonstrates that genuine multipartite entanglement in Gaussian states can be inferred solely from local separable marginals, using a novel entanglement witness and an experimentally feasible scheme.

Contribution

It introduces a method to detect global multipartite entanglement from local marginals in Gaussian states, advancing quantum diagnostics.

Findings

Multipartite entanglement can be inferred from local marginals.

A genuine multipartite entanglement witness was constructed.

An experimental scheme for three-mode state preparation was proposed.

Abstract

Genuine multipartite entanglement underlies correlation experiments corroborating quantum mechanics and it is an expedient empowering many quantum technologies. One of many counterintuitive facets of genuine multipartite entanglement is its ability to exhibit an emergent character, that is, one can infer its presence in some multipartite states merely from a set of its separable marginals. Here, we show that the effect can be found also in the context of Gaussian states of bosonic systems. Specifically, we construct examples of multimode Gaussian states carrying genuine multipartite entanglement which can be verified solely from separable nearest-neighbour two-mode marginals. The key tool of our construction is a genuine multipartite entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semi-definite programme. We also propose an experimental scheme for preparation of the simplest three-mode state, which requires interference of three correlatively displaced squeezed beams on two beam splitters. Besides revealing the concept of emergent genuine multipartite entanglement in the Gaussian scenario and bringing it closer to experimentally testable form, our results pave the way to effective diagnostics methods of global properties of multipartite states without complete tomography.