{"paper":{"title":"A note about claw function with a small range","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Andris Ambainis, J\\=anis Iraids, Kaspars Balodis","submitted_at":"2021-03-30T14:30:35Z","abstract_excerpt":"In the claw detection problem we are given two functions $f:D\\rightarrow R$ and $g:D\\rightarrow R$ ($|D|=n$, $|R|=k$), and we have to determine if there is exist $x,y\\in D$ such that $f(x)=g(y)$. We show that the quantum query complexity of this problem is between $\\Omega\\left(n^{1/2}k^{1/6}\\right)$ and $O\\left(n^{1/2+\\varepsilon}k^{1/4}\\right)$ when $2\\leq k<n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.16390","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.16390/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"}