{"paper":{"title":"The quantum query complexity of approximating the median and related statistics","license":"","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Ashwin Nayak, Felix Wu","submitted_at":"1998-04-29T02:00:07Z","abstract_excerpt":"Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \\epsilon > 0, we say that x_i is an \\epsilon-approximate median if the number of elements strictly less than x_i, and the number of elements strictly greater than x_i are each less than (1+\\epsilon)n/2. We consider the quantum query complexity of computing an \\epsilon-approximate median, given the sequence X as an oracle. We prove a lower bound of \\Omega(\\min{{1/\\epsilon},n}) queries for any quantum algorithm that computes an \\epsilon-approximate median with any constant probability greater than 1/2. We also show how an \\epsilon-approx"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9804066","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/9804066/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"}