{"paper":{"title":"Quantum lower bound for inverting a permutation with advice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.CR"],"primary_cat":"quant-ph","authors_text":"Aleksandrs Belovs, Aran Nayebi, Luca Trevisan, Scott Aaronson","submitted_at":"2014-08-14T04:56:23Z","abstract_excerpt":"Given a random permutation $f: [N] \\to [N]$ as a black box and $y \\in [N]$, we want to output $x = f^{-1}(y)$. Supplementary to our input, we are given classical advice in the form of a pre-computed data structure; this advice can depend on the permutation but \\emph{not} on the input $y$. Classically, there is a data structure of size $\\tilde{O}(S)$ and an algorithm that with the help of the data structure, given $f(x)$, can invert $f$ in time $\\tilde{O}(T)$, for every choice of parameters $S$, $T$, such that $S\\cdot T \\ge N$. We prove a quantum lower bound of $T^2\\cdot S \\ge \\tilde{\\Omega}(\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3193","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"}