We prove that for every Bell’s inequality, including those which are not yet known, there always exists a communication complexity problem, for which a protocol assisted by states which violate the inequality is more efficient than any classical protocol. Violation of Bell’s inequalities is the necessary and sufficient condition for quantum protocol to beat the classical ones.

• Received 21 October 2002

DOI:https://doi.org/10.1103/PhysRevLett.92.127901