  Based on a geometrical argument introduced by Zukowski, a new multisetting
Bell inequality is derived, for the scenario in which many parties make
measurements on two-level systems. This generalizes and unifies some previous
results. Moreover, a necessary and sufficient condition for the violation of
this inequality is presented. It turns out that the class of non-separable
states which do not admit local realistic description is extended when compared
to the two-setting inequalities. However, supporting the conjecture of Peres,
quantum states with positive partial transposes with respect to all subsystems
do not violate the inequality. Additionally, we follow a general link between
Bell inequalities and communication complexity problems, and present a quantum
protocol linked with the inequality, which outperforms the best classical
protocol.
