  The strength of classical correlations is subject to certain constraints,
commonly known as Bell inequalities. Violation of these inequalities is the
manifestation of nonlocality---displayed, in particular, by quantum mechanics,
meaning that quantum mechanics can outperform classical physics at tasks
associated with such Bell inequalities. Interestingly, however, there exist
situations in which this is not the case. We associate an intriguing class of
bound entangled states, constructed from unextendable product bases (UPBs) with
a wide family of tasks, for which (i) quantum correlations do not outperform
the classical ones but (ii) there exist supraquantum nonsignalling correlations
that do provide an advantage.
