### Abstract

It is well-known that multipartite entanglement has a considerably richer structure than its bipartite counterpart. For instance, already in the tripartite setting, one can find entangled quantum state that is separable with respect to all bipartitions --- this gives rise to some kind of "invisible entanglement" since the entanglement cannot be associated with any subset of the parties. Here, we present a four-partite analog of this phenomenon at the level of correlations (probability distributions). In particular, we provide an example of four-partite quantum probability distributions where all the tripartite marginals are provably local (in the sense of non-Bell-inequality-violating) but where the four-partite distributions can be shown to exhibit genuine three-way nonlocality.