Quantifying multipartite nonlocality

The nonlocal correlations of multipartite entangled states can be reproduced by a classical model if sufficiently many parties join together or if sufficiently many parties broadcast their measurement inputs. The maximal number m of groups and the minimal number k of broadcasting parties that allow for the reproduction of a given set of correlations quantify their multipartite nonlocal content. We show how upper-bounds on m and lower-bounds on k can be computed from the violation of the Mermin-Svetlichny inequalities. While n-partite GHZ states violate these inequalities maximally, we find that W states violate them only by a very small amount.