{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZYSL557ZIZSU6G2FQJ77XMBSQK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1dd23ebdef3668e761980969b4009b8150a2f9aded28c26b75c5fcccdd2949a8","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-09-26T19:44:23Z","title_canon_sha256":"ade635f05454fd1b550446025211cbebcc9d748351bee4d3f89923aa76cfce0f"},"schema_version":"1.0","source":{"id":"quant-ph/0509181","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0509181","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0509181v3","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0509181","created_at":"2026-05-18T04:09:36Z"},{"alias_kind":"pith_short_12","alias_value":"ZYSL557ZIZSU","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZYSL557ZIZSU6G2F","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZYSL557Z","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:46f74d81afa52dfbb95e3619c5434b2769af963d2d30d01f15c2c74260dbadf8","target":"graph","created_at":"2026-05-18T04:09:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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)","authors_text":"Shengyu Zhang, Wei Huang, Yaoyun Shi, Yufan Zhu","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-09-26T19:44:23Z","title":"The Communication Complexity of the Hamming Distance Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0509181","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7231d91da64200cbb5257592233d3fddb1c8d203aa893a2c89f351afc2ca8282","target":"record","created_at":"2026-05-18T04:09:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1dd23ebdef3668e761980969b4009b8150a2f9aded28c26b75c5fcccdd2949a8","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-09-26T19:44:23Z","title_canon_sha256":"ade635f05454fd1b550446025211cbebcc9d748351bee4d3f89923aa76cfce0f"},"schema_version":"1.0","source":{"id":"quant-ph/0509181","kind":"arxiv","version":3}},"canonical_sha256":"ce24bef7f946654f1b45827ffbb03282819cb0fba7cfe29756da4caee98c78af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce24bef7f946654f1b45827ffbb03282819cb0fba7cfe29756da4caee98c78af","first_computed_at":"2026-05-18T04:09:36.516665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:36.516665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AosCtja29bG7ajbWArrF6ccMY6jgXc5dnordlIFMpPECsTXav1FT2z6Jf0CQb/b20AVTGifRNrUftpO2Ygm8BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:36.517095Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0509181","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7231d91da64200cbb5257592233d3fddb1c8d203aa893a2c89f351afc2ca8282","sha256:46f74d81afa52dfbb95e3619c5434b2769af963d2d30d01f15c2c74260dbadf8"],"state_sha256":"a92d953ed7f069e90d3aa7cf5e4f00f72366c305ed0f403bba7cb901f7bda1cd"}