The Communication Complexity of the Hamming Distance Problem
摘要
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).
引用
@article{arxiv.quant-ph/0509181,
title = {The Communication Complexity of the Hamming Distance Problem},
author = {Wei Huang and Yaoyun Shi and Shengyu Zhang and Yufan Zhu},
journal= {arXiv preprint arXiv:quant-ph/0509181},
year = {2011}
}
备注
8 pages, v3, updated reference. to appear in Information Processing Letters, 2006