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

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

2006-07-25

arxiv.org/abs/quant-ph/0607173v1

Physics

Quantum Physics

Scientific paper

We give a tight lower bound of Omega(\sqrt{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(\log n) 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 coefficients inequality of Kahn Kalai and Linial [KKL88].

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