Quantum multiparty communication complexity and circuit lower bounds

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Omega(n/2(k)), its classical k-party communication is Omega(n/2(k/2)). Finding such an f would allow us to prove strong classical lower bounds for k >= log n players and make progress towards solving a major open question about symmetric circuits.