{"paper":{"title":"Lifting randomized query complexity to randomized communication complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Anurag Anshu, Naresh B. Goud, Priyanka Mukhopadhyay, Rahul Jain, Srijita Kundu","submitted_at":"2017-03-22T04:45:51Z","abstract_excerpt":"We show that for a relation $f\\subseteq \\{0,1\\}^n\\times \\mathcal{O}$ and a function $g:\\{0,1\\}^{m}\\times \\{0,1\\}^{m} \\rightarrow \\{0,1\\}$ (with $m= O(\\log n)$), $$\\mathrm{R}_{1/3}(f\\circ g^n) = \\Omega\\left(\\mathrm{R}_{1/3}(f) \\cdot \\left(\\log\\frac{1}{\\mathrm{disc}(M_g)} - O(\\log n)\\right)\\right),$$ where $f\\circ g^n$ represents the composition of $f$ and $g^n$, $M_g$ is the sign matrix for $g$, $\\mathrm{disc}(M_g)$ is the discrepancy of $M_g$ under the uniform distribution and $\\mathrm{R}_{1/3}(f)$ ($\\mathrm{R}_{1/3}(f\\circ g^n)$) denotes the randomized query complexity of $f$ (randomized comm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07521","kind":"arxiv","version":5},"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"}