{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GNLHAT5YG3J7NTWDUSOHFZ4J7S","short_pith_number":"pith:GNLHAT5Y","schema_version":"1.0","canonical_sha256":"3356704fb836d3f6cec3a49c72e789fca33e9a418f80fc02cdf679b399aa9e9f","source":{"kind":"arxiv","id":"1307.6738","version":1},"attestation_state":"computed","paper":{"title":"Efficient quantum protocols for XOR functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Shengyu Zhang","submitted_at":"2013-07-25T13:37:44Z","abstract_excerpt":"We show that for any Boolean function f on {0,1}^n, the bounded-error quantum communication complexity of XOR functions $f\\circ \\oplus$ satisfies that $Q_\\epsilon(f\\circ \\oplus) = O(2^d (\\log\\|\\hat f\\|_{1,\\epsilon} + \\log \\frac{n}{\\epsilon}) \\log(1/\\epsilon))$, where d is the F2-degree of f, and $\\|\\hat f\\|_{1,\\epsilon} = \\min_{g:\\|f-g\\|_\\infty \\leq \\epsilon} \\|\\hat f\\|_1$. This implies that the previous lower bound $Q_\\epsilon(f\\circ \\oplus) = \\Omega(\\log\\|\\hat f\\|_{1,\\epsilon})$ by Lee and Shraibman \\cite{LS09} is tight for f with low F2-degree. The result also confirms the quantum version o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.6738","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2013-07-25T13:37:44Z","cross_cats_sorted":[],"title_canon_sha256":"5a11f02acc00344a5cffde51e5c91c1693ae337b6c47b0eec3c1cd24a0dc88c4","abstract_canon_sha256":"c6b29d8a0da338fa6595ac94b636375e3cc6fe0fdf1a7533e26f1b741ff3fdf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:34.817864Z","signature_b64":"kXD985e5UIqVPJWuSrVKQc0qOMksM1T4dCoKWRgAGHangVqaURGaFggYy/Ry7yQMiM9EEjSwTUiLy/tL9lD1Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3356704fb836d3f6cec3a49c72e789fca33e9a418f80fc02cdf679b399aa9e9f","last_reissued_at":"2026-05-18T03:17:34.817240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:34.817240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient quantum protocols for XOR functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Shengyu Zhang","submitted_at":"2013-07-25T13:37:44Z","abstract_excerpt":"We show that for any Boolean function f on {0,1}^n, the bounded-error quantum communication complexity of XOR functions $f\\circ \\oplus$ satisfies that $Q_\\epsilon(f\\circ \\oplus) = O(2^d (\\log\\|\\hat f\\|_{1,\\epsilon} + \\log \\frac{n}{\\epsilon}) \\log(1/\\epsilon))$, where d is the F2-degree of f, and $\\|\\hat f\\|_{1,\\epsilon} = \\min_{g:\\|f-g\\|_\\infty \\leq \\epsilon} \\|\\hat f\\|_1$. This implies that the previous lower bound $Q_\\epsilon(f\\circ \\oplus) = \\Omega(\\log\\|\\hat f\\|_{1,\\epsilon})$ by Lee and Shraibman \\cite{LS09} is tight for f with low F2-degree. The result also confirms the quantum version o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6738","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.6738","created_at":"2026-05-18T03:17:34.817346+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.6738v1","created_at":"2026-05-18T03:17:34.817346+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6738","created_at":"2026-05-18T03:17:34.817346+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNLHAT5YG3J7","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNLHAT5YG3J7NTWD","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNLHAT5Y","created_at":"2026-05-18T12:27:45.050594+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S","json":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S.json","graph_json":"https://pith.science/api/pith-number/GNLHAT5YG3J7NTWDUSOHFZ4J7S/graph.json","events_json":"https://pith.science/api/pith-number/GNLHAT5YG3J7NTWDUSOHFZ4J7S/events.json","paper":"https://pith.science/paper/GNLHAT5Y"},"agent_actions":{"view_html":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S","download_json":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S.json","view_paper":"https://pith.science/paper/GNLHAT5Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.6738&json=true","fetch_graph":"https://pith.science/api/pith-number/GNLHAT5YG3J7NTWDUSOHFZ4J7S/graph.json","fetch_events":"https://pith.science/api/pith-number/GNLHAT5YG3J7NTWDUSOHFZ4J7S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S/action/storage_attestation","attest_author":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S/action/author_attestation","sign_citation":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S/action/citation_signature","submit_replication":"https://pith.science/pith/GNLHAT5YG3J7NTWDUSOHFZ4J7S/action/replication_record"}},"created_at":"2026-05-18T03:17:34.817346+00:00","updated_at":"2026-05-18T03:17:34.817346+00:00"}