{"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"}