Bell's inequalities and quantum communication complexity

The study showed that the necessary and sufficient condition for quantum protocols to have a higher success rate than any classical protocol is that the state violates a Bell inequality. For every Bell inequality, it was shown that, there always exists a communication complexity problem (CCP), for which the protocol assisted by states which violate the inequality is more efficient than any classical protocol. A quantum competitor was introduced before showing the maximum probability of success in a protocol. It was also shown that the results could be generalized to Bell inequalities with higher-dimensional systems and more measurement settings.