The one-way communication complexity of the Boolean Hidden Matching Problem

We give a tight lower bound of ( p n) for the randomized one-way communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since there is a quantum one-way communication complexity protocol of O(logn) qubits for this problem, we obtain an exponential separation of quantum and classical one-way communication complexity for partial functions. A similar result was independently obtained by Gavinsky, Kempe, de Wolf [GKdW06]. Our lower bound is obtained by Fourier analysis, using the Fourier coecients inequality of Kahn Kalai and Linial [KKL88].

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