Near-Optimal Bounds on Bounded-Round Quantum Communication Complexity of Disjointness

Abstract

We prove a near optimal round-communication trade off for the two-party quantum communication complexity of disjointness. For protocols with r rounds, we prove a lower bound of Ω(n/r) on the communication required for computing disjointness of input size n, which is optimal up to logarithmic factors. The previous best lower bound was Ω(n/r2) due to Jain, Radha krishnan and Sen. Along the way, we develop several tools for quantum information complexity, one of which is a lower bound for quantum information complexity in terms of the generalized discrepancy method. As a corollary, we get that the quantum communication complexity of any boolean function f is at most 2O(QIC(f)), where QIC(f) is the prior-free quantum information complexity of f (with error 1/3).