{"paper":{"title":"Quantum communication complexity of symmetric predicates","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Alexander Razborov","submitted_at":"2002-04-04T22:49:34Z","abstract_excerpt":"We completely (that is, up to a logarithmic factor) characterize the bounded-error quantum communication complexity of every predicate $f(x,y)$ depending only on $|x\\cap y|$ ($x,y\\subseteq [n]$). Namely, for a predicate $D$ on $\\{0,1,...,n\\}$ let $\\ell_0(D)\\df \\max\\{\\ell : 1\\leq\\ell\\leq n/2\\land D(\\ell)\\not\\equiv D(\\ell-1)\\}$ and $\\ell_1(D)\\df \\max\\{n-\\ell : n/2\\leq\\ell < n\\land D(\\ell)\\not\\equiv D(\\ell+1)\\}$. Then the bounded-error quantum communication complexity of $f_D(x,y) = D(|x\\cap y|)$ is equal (again, up to a logarithmic factor) to $\\sqrt{n\\ell_0(D)}+\\ell_1(D)$. In particular, the com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0204025","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":""},"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"}