  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.
