Certifying emergent genuine multipartite entanglement with a partially blind witness

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 also be found 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 -neighbor two-mode marginals. The key tool of our construction is an entanglement witness acting only on some two-mode reductions of the global covariance matrix, which we find by a numerical solution of a semidefinite program. 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.

Automated summary

This paper investigates genuine multipartite entanglement in Gaussian states and proposes a method to verify this entanglement solely from separable two-mode marginals. Examples of Gaussian states carrying genuine multipartite entanglement are constructed, and an experimental scheme for preparing the simplest three-mode state is proposed. These results not only reveal a new concept of entanglement in the Gaussian scenario, but also pave the way for effective diagnostics methods of global properties of multipartite states.