{"paper":{"title":"Quantum-Proof Extractors: Optimal up to Constant Factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Gil Cohen, Kai-Min Chung, Thomas Vidick, Xiaodi Wu","submitted_at":"2016-05-13T14:42:05Z","abstract_excerpt":"We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence $O(\\log(n/\\varepsilon))$ on the input length $n$ and error $\\varepsilon$. Our extractors support any min-entropy $k=\\Omega(\\log{n} + \\log^{1+\\alpha}(1/\\varepsilon))$ and extract $m=(1-\\alpha)k$ bits that are $\\varepsilon$-close to uniform, for any desired constant $\\alpha > 0$. Previous constructions had a quadratically worse seed length or were restricted to very large input min-entropy or very few output bits.\n  Our result is based on a generic reduction showing that any strong clas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04194","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"}