{"paper":{"title":"The Communication Complexity of the Hamming Distance Problem","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Shengyu Zhang, Wei Huang, Yaoyun Shi, Yufan Zhu","submitted_at":"2005-09-26T19:44:23Z","abstract_excerpt":"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)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0509181","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}