Certifying nonlocality from separable marginals

Imagine three parties, Alice, Bob, and Charlie, who share a state of three qubits such that all two-party reduced states A-B,A-C, and B-C are separable. Suppose that they have information only about these marginals but not about the global state. According to recent results, there exists an example for a set of three separable two-party reduced states that is only compatible with an entangled global state. In this paper, we show a stronger result, by exhibiting separable two-party reduced states A-B, A-C, and B-C, such that any global state compatible with these marginals is nonlocal. Hence, we obtain that nonlocality of multipartite states can be certified from information only about separable marginals.