{
  "abstract": "Quantum private broadcasting (\\textsf{QPB}) asks whether a quantum message can be encrypted once, broadcast to several recipients, and decrypted locally while the joint ciphertext reveals no plaintext information. Broadbent, González-Guillén, and Schuknecht showed that the full tensor-power space \\(\\mathcal H_d^{\\otimes t}\\) is generally unsuitable for \\textsf{QPB}, identified \\(\\mathrm{Sym}^t(\\mathcal H_d)\\) as a natural plaintext space, introduced symmetric unitary \\(t\\)-designs, and asked which other subspaces support private broadcast. Using Schur-Weyl duality, we classify all subspaces \\(\\mathcal S\\subseteq\\mathcal H_d^{\\otimes t}\\) on which the collective Haar twirl \\(\\mathcal T^{(t)}\\) is a replacement channel. Precisely, every Schur-Weyl block weight must be independent of the encoded state, and in each active block \\(V_λ\\otimes W_λ\\), the reduced state on the multiplicity space \\(W_λ\\) must be fixed. This yields explicit two-block and general multiblock constructions and realizes the classification as the Schur-Weyl form of the Knill-Laflamme conditions for a complementary channel of \\(\\mathcal T^{(t)}\\). We also introduce a canonical reduction under deletion of a recipient and characterize privacy heredity, design heredity, and \\textsf{QPB}-heredity for exact restricted designs. The symmetric tower is fully \\textsf{QPB}-hereditary, whereas the antisymmetric tower is fully privacy-hereditary and is design-hereditary from level \\(s\\) to \\(s-1\\) exactly when \\(s\\leq(d+1)/2\\). For canonical carriers in arbitrary Schur-Weyl blocks, hereditary reduction is governed by multiplicity-free branching along the Young graph and inclusion of the associated Peter-Weyl coefficient spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33553",
  "author_total": 1,
  "authors": [
    {
      "name": "Sayantan Ganguly"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bexrp331e39et.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33553",
  "fulltext_url": null,
  "id": "bexrp331e39et",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33553",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7223976772",
  "pdf_url": "https://arxiv.org/pdf/2610.33553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bexrp331e39et.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Admissible Subspaces for the Collective Haar Twirl: Schur-Weyl Classification and Heredity under Tensor-Factor Reduction",
  "title_text": "Admissible Subspaces for the Collective Haar Twirl: Schur-Weyl Classification and Heredity under Tensor-Factor Reduction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/bexrp331e39et",
  "venue": "arXiv",
  "versions": []
}