  We investigate the scenario where spatially separated parties perform
measurements in randomly chosen bases on an N-partite
Greenberger-Horne-Zeilinger state. We show that without any alignment of the
measurements, the observers will obtain correlations that violate a Bell
inequality with a probability that rapidly approaches 1 as N increases and that
this probability is robust against noise. We also prove that restricting these
randomly chosen measurements to a plane perpendicular to a common direction
will always generate correlations that violate some Bell inequality.
Specifically, if each observer chooses their two measurements to be locally
orthogonal, then the N observers will violate one of two Bell inequalities by
an amount that increases exponentially with N. These results are also robust
against noise and perturbations of each observer's reference direction from the
common direction.
