Multiparty Quantum Communication Complexity

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function f . The communication complexity of f is the minimum number of classical bits required to be broadcasted for every party to know the value of f on their inputs. We construct a function G such that for the one-round communication model and three parties, G can be computed with n + 1 bits of communication when the parties share prior entanglement. We then show that without entangled particles, the one-round communication complexity of G is (3/2)n+1. Next we generalize this function to a function F . We show that if the parties share prior quantum entanglement, then the communication complexity of F is exactly k. We also show that if no entangled particles are provided, then the communication complexity of F is roughly k log 2 k. These two results prove for the first time communication complexity separations better than a constant number of bits. PACS numbers: 03.67.Hk