We prove that for every Bell's inequality and for a broad class of protocols,
there always exists a multi-party communication complexity problem, for which
the protocol assisted by states which violate the inequality is more efficient
than any classical protocol. Moreover, for that advantage Bell's inequality
violation is a necessary and sufficient criterion. Thus, violation of Bell's
inequalities has a significance beyond that of a non-optimal-witness of
non-separability.Comment: 4 pages, 1 figur