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 Ω( n 2k ), then its classical k-party communication is Ω( n 2k/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 main open question about symmetric circuits.