Nonlocality distillation and quantum voids

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource, distillation protocols also play an important role in the understanding of information-theoretical principles for quantum theory. Here, we derive a necessary condition for nonlocality distillation from two copies and apply it, among other results, to show that one-dimensional (1D) and 2D quantum voids---faces of the nonlocal simplex set with no quantum realization---can be distilled up to PR boxes. With that, we generalize previous results in the literature, for instance, showing a broad class of postquantum correlations that make communication complexity trivial and violate the information causality principle.