{
  "abstract": "We consider the computational task of anti-symmetrization of an unknown mixed quantum state: Given iid copies of a rank-$r$ qudit state $ρ=\\sum_{i=1}^r λ_i |φ_i\\rangle\\!\\langleφ_i|$, prepare a copy of the state proportional to $Π_{\\mathrm{anti}}^r (|φ_1\\rangle\\otimes \\ldots\\otimes|φ_r\\rangle)$, with $Π_{\\mathrm{anti}}^r$ the anti-symmetric subspace projector. We first give a simple algorithm for anti-symmetrization that uses $\\widetilde{O}(r / λ_{\\min})$ copies of $ρ$, where $λ_{\\min}$ is the minimum non-zero eigenvalue of $ρ$. This algorithm works even in the streaming setting with small working memory, and it uses only simple quantum operations like controlled-SWAPs and constantly many layers of single-qubit gates. As an application of this streaming anti-symmetrization procedure, we give a reduction from gapped mixed-state one-way state generators to pure-state one-way state generators. Then, using tools from Schur-Weyl duality, we give and analyze a second (non-streaming) anti-symmetrization procedure that uses $O(r / λ_{\\min})$ copies of $ρ$, which then serves as a building block in new algorithms for weak Schur sampling and unitary Schur sampling, outperforming existing approaches in some regimes of number of copies $n$ and local dimension $d$, as well as in an algorithm for optimal purity amplification for qudit states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06737",
  "author_total": 6,
  "authors": [
    {
      "name": "Adam Bene Watts"
    },
    {
      "name": "John Bostanci"
    },
    {
      "name": "Matthias C. Caro"
    },
    {
      "name": "Daniel Grier"
    },
    {
      "name": "Sihan Liu"
    },
    {
      "name": "Gaurav Mahajan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fc00t43p84wng.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06737",
  "fulltext_url": null,
  "id": "fc00t43p84wng",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06737",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220733266",
  "pdf_url": "https://arxiv.org/pdf/2610.06737",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fc00t43p84wng.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06737",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06737"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Anti-symmetrization is cheap and useful",
  "title_text": "Anti-symmetrization is cheap and useful",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/fc00t43p84wng",
  "venue": "arXiv",
  "versions": []
}