  A deeper understanding of the origin of quantum correlations is expected to
shred light on the physical principles underlying quantum mechanics. In this
work, we reconsider the possibility of devising "crypto-nonlocal theories",
using a terminology firstly introduced by Leggett. We generalize and simplify
the investigations on this subject which can be found in the literature. At
their deeper level, such theories allow nonlocal correlations which can
overcome the quantum limit.
