{
  "abstract": "We give elementary proofs of the $Ω(n^{2/3})$ quantum query lower bound for element distinctness and the $Ω(n^{k/(k+1)})$ lower bound for the $k$-sum problem, for fixed $k$ and sufficiently large groups. The proofs use only basic properties of quantum states and linear algebra, analyzing the differences of algorithm states on different inputs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32693",
  "author_total": 2,
  "authors": [
    {
      "name": "Andris Ambainis"
    },
    {
      "name": "Martins Kokainis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4v992vh2bqt1v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32693",
  "fulltext_url": null,
  "id": "4v992vh2bqt1v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32693",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7223679833",
  "pdf_url": "https://arxiv.org/pdf/2610.32693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4v992vh2bqt1v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2610.32693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32693"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Elementary proofs of quantum lower bounds for element distinctness and k-sum",
  "title_text": "Elementary proofs of quantum lower bounds for element distinctness and k-sum",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/4v992vh2bqt1v",
  "venue": "arXiv",
  "versions": []
}