{
  "abstract": "Schur sampling is a fundamental primitive for extracting permutation-invariant information from many-body quantum systems and has broad applications in quantum information science. Circuit-based implementations typically rely on coherent representation-theoretic operations such as Clebsch-Gordan transforms, generalized phase estimation, or quantum Fourier transforms over the symmetric group. We show that unitary Schur sampling of arbitrary permutation-invariant mixed states on $n$ $d$-dimensional qudits can instead be implemented using only pairwise SWAP tests, namely, two-qudit projective measurements onto the symmetric and antisymmetric subspaces. Our protocol achieves error $ε$ in diamond distance using $O(n\\min\\{n,d\\}^{3}\\log^2(n/ε))$ random SWAP tests. The central idea is to repeatedly identify and extract the largest antisymmetric subsystem. This turns unitary Schur sampling into a search for antisymmetry and gives the algorithm a natural interpretation as a stochastic traversal of a Young diagram. The protocol preserves the $\\mathrm{SU}(d)$-irrep state while preparing a canonical pure state in the multiplicity subsystem. As an application, we consider quantum purity amplification (QPA), in which multiple noisy copies of a pure quantum state are combined to produce a state of higher purity. We show that the optimal purified state can be obtained by retaining a single designated output qudit and discarding the rest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02103",
  "author_total": 4,
  "authors": [
    {
      "name": "Shrigyan Brahmachari"
    },
    {
      "name": "David Jakab"
    },
    {
      "name": "Henry D. Pfister"
    },
    {
      "name": "Iman Marvian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5dm0x32bmfevz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02103",
  "fulltext_url": null,
  "id": "5dm0x32bmfevz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02103",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215732663",
  "pdf_url": "https://arxiv.org/pdf/2610.02103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5dm0x32bmfevz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.02103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Unitary Schur Sampling of Qudits via Random SWAP Tests: Hunt for Antisymmetry",
  "title_text": "Unitary Schur Sampling of Qudits via Random SWAP Tests: Hunt for Antisymmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/5dm0x32bmfevz",
  "venue": "arXiv",
  "versions": []
}