Implications of communication complexity in multipartite systems

We present a class of noisy N -partite nonlocal boxes which reduces all communication complexity problems of N parties to triviality. The noise level is constant for any number of parties and gives a probability of simulating the nonlocal box only slightly higher than that of quantum mechanics. Intriguingly, this class of multipartite nonlocal boxes corresponds to the Bell-Svetlichny inequality, which manifests genuine multipartite nonseparability. These results provide further support for the recent conjecture by Brassard, [Phys. Rev. Lett. 96, 250401 (2006)] that had nature been more nonlocal than quantum mechanics allows, communication complexity would have been trivial.