  We address the question of when quantum entanglement is a useful resource for
information processing tasks by presenting a new class of nonlocal games that
are simple, direct, generalizations of the Clauser Horne Shimony Holt game. For
some ranges of the parameters that specify the games, quantum mechanics offers
an advantage, while, surprisingly, for others quantum mechanics is no more
powerful than classical mechanics in performing the nonlocal task. This sheds
new light on the difference between classical, quantum and super-quantum
correlations.
