  We give the first exponential separation between quantum and classical
multi-party communication complexity in the (non-interactive) one-way and
simultaneous message passing settings.
  For every k, we demonstrate a relational communication problem between k
parties that can be solved exactly by a quantum simultaneous message passing
protocol of cost O(log n) and requires protocols of cost n^{c/k^2}, where c>0
is a constant, in the classical non-interactive one-way message passing model
with shared randomness and bounded error.
  Thus our separation of corresponding communication classes is superpolynomial
as long as k=o(\sqrt{\log n / \log\log n}) and exponential for k=O(1).
