Quantum multiparty communication complexity and circuit lower bounds

Abstract

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), 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 major open question about symmetric circuits.