Nonlocal multipartite correlations from local marginal probabilities

Understanding what can be inferred about a multiparticle quantum system given only the knowledge of its subparts is a highly nontrivial task. Clearly, if a global system does not contain an information resource of some kind, neither do its subparts. For the case of entanglement as an information resource, it is known that the converse of this last statement is not true: Some nonentangled reduced states are only compatible with global states which are entangled. We extend this result to correlations and provide local marginal correlations that are only compatible with global genuinely tripartite nonlocal correlations. Quantum nonlocality can thus be deduced from the mere observation of local marginal correlations.