Exploring nonlocal correlations in many-body systems

While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: such inequalities usually rely on expectation values involving many parties and require an individual addressing of each party. A recent work [J. Tura et al. Science 344, 6189 (2014)] proposed simpler Bell inequalities overcoming such difficulties, opening the way for the detection of Bell correlations with trusted collectiWe address the question of how to evaluate the Bell correlations depth, i.e. the number of parties sharing genuinely nonlocal correlations in a multipartite system. Previous work has shown that it is possible to construct inequalities based on two-body symmetric correlation functions that can reveal k-nonlocality, but only for $k\leq6$. We extend this result up to k