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

Exponential Separation of Quantum and Classical Non-Interactive Multi-Party Communication Complexity