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We show that the t-party k-round communication complexity of F is Omega(s_m(f_F)/(k^2)), where s_m(f_F) stands for the `monotone sensitivity of f_F' and is defined by s_m(f_F) \\defeq max_{S\\subseteq [n]} |{i: f_F(S \\cup {i}) \\neq f_F(S)|. For two-party quantum communication protocols for the set disjointness problem, this implies that the two par"},"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":"quant-ph/0303138","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-03-22T08:07:45Z","cross_cats_sorted":[],"title_canon_sha256":"80a47c3eea010e22ca7796f5605fe9e4796187a9f2e6f91e5313eb90b4297d11","abstract_canon_sha256":"326db60785f3d27c11394fa4b0f6a749f091659e8284278843c93d650c19db47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:46:08.822152Z","signature_b64":"wMbXbBLk9zqtOe1RGHjzkoPIiQj2Is3HPHGaIklQ4MfIffmn4dE08u/7wblJ1on0NHLKb9yRaLtFT1CNdufOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ef79c423adfa91b0e0d8af86f82b7b0affc679c63bd3361d8e9d6b938d7554","last_reissued_at":"2026-07-04T14:46:08.821803Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:46:08.821803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lower bound for bounded round quantum communication complexity of set disjointness","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jaikumar Radhakrishnan, Pranab Sen, Rahul Jain","submitted_at":"2003-03-22T08:07:45Z","abstract_excerpt":"We consider the class of functions whose value depends only on the intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class there is an f_F: 2^{[n]} \\to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1 \\cap X_2 \\cap ... \\cap X_t). We show that the t-party k-round communication complexity of F is Omega(s_m(f_F)/(k^2)), where s_m(f_F) stands for the `monotone sensitivity of f_F' and is defined by s_m(f_F) \\defeq max_{S\\subseteq [n]} |{i: f_F(S \\cup {i}) \\neq f_F(S)|. For two-party quantum communication protocols for the set disjointness problem, this implies that the two par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0303138","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/0303138/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"quant-ph/0303138","created_at":"2026-07-04T14:46:08.821862+00:00"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0303138v2","created_at":"2026-07-04T14:46:08.821862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0303138","created_at":"2026-07-04T14:46:08.821862+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHXXTRBDVX5J","created_at":"2026-07-04T14:46:08.821862+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHXXTRBDVX5JDMHA","created_at":"2026-07-04T14:46:08.821862+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHXXTRBD","created_at":"2026-07-04T14:46:08.821862+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08517","citing_title":"Quantum Communication Lower Bounds for Search Problems via Matrix Discrepancy","ref_index":55,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM","json":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM.json","graph_json":"https://pith.science/api/pith-number/QHXXTRBDVX5JDMHA3CXYN6BLPM/graph.json","events_json":"https://pith.science/api/pith-number/QHXXTRBDVX5JDMHA3CXYN6BLPM/events.json","paper":"https://pith.science/paper/QHXXTRBD"},"agent_actions":{"view_html":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM","download_json":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM.json","view_paper":"https://pith.science/paper/QHXXTRBD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=quant-ph/0303138&json=true","fetch_graph":"https://pith.science/api/pith-number/QHXXTRBDVX5JDMHA3CXYN6BLPM/graph.json","fetch_events":"https://pith.science/api/pith-number/QHXXTRBDVX5JDMHA3CXYN6BLPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM/action/storage_attestation","attest_author":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM/action/author_attestation","sign_citation":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM/action/citation_signature","submit_replication":"https://pith.science/pith/QHXXTRBDVX5JDMHA3CXYN6BLPM/action/replication_record"}},"created_at":"2026-07-04T14:46:08.821862+00:00","updated_at":"2026-07-04T14:46:08.821862+00:00"}