{"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"}