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We present an exhaustive numerical analysis of violations of local realism byfamilies of multipartite quantum states. As an indicator of nonclassicality weemploy the probability of violation for randomly sampled observables.Surprisingly, it rapidly increases with the number of parties or settings andeven for relatively small values local realism is violated for almost allobservables. We have observed this effect to be typical in the sense that itemerged for all investigated states including some with randomly drawncoefficients. We also present the probability of violation as a witness ofgenuine multipartite entanglement.

Multipartite nonlocality and random measurements