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The Communication Complexity of the Hamming Distance Problem

Wei Huang·Yaoyun Shi·Shengyu Zhang·Yufan Zhu
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Abstract

We investigate the randomized and quantum communication complexity of the Hamming Distance problem, which is to determine if the Hamming distance between two n-bit strings is no less than a threshold d. We prove a quantum lower bound of \Omega(d) qubits in the general interactive model with shared prior entanglement. We also construct a classical protocol of O(d \log d) bits in the restricted Simultaneous Message Passing model, improving previous protocols of O(d^2) bits (A. C.-C. Yao, Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pp. 77-81, 2003), and O(d\log n) bits (D. Gavinsky, J. Kempe, and R. de Wolf, quant-ph/0411051, 2004).

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Wei Huang, Yaoyun Shi, Shengyu Zhang, Yufan Zhu. 2005-09-26. The Communication Complexity of the Hamming Distance Problem. https://doi.org/10.1016/j.ipl.2006.01.014

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