{
  "abstract": "We establish an exact equivalence in distribution between $D$-dimensional random mixed states induced by partial traces over $K$-dimensional environments and the Mai-Alquier distribution, a mixture of $K$ independent Haar-random pure states weighted by a symmetric Dirichlet distribution. This identification recasts a class of expectation values for induced ensembles into calculations involving Dirichlet moments and low-order Haar averages on a single-system state space. As applications, we recover exact purity moments up to fourth order, derive the mean Hilbert--Schmidt distance between independent induced ensembles with possibly different environment dimensions, and obtain exact average determinants. These results provide a unified and constructive perspective on induced random mixed states and on the evaluation of quantities such as purity moments, overlaps, and determinants.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09421",
  "author_total": 4,
  "authors": [
    {
      "name": "Brian T. Kirby"
    },
    {
      "name": "Alexander C. B. Greenwood"
    },
    {
      "name": "Sanjaya Lohani"
    },
    {
      "name": "Joseph M. Lukens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/76dsm4tk7m2v4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09421",
  "fulltext_url": null,
  "id": "76dsm4tk7m2v4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09421",
  "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",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7212109145",
  "pdf_url": "https://arxiv.org/pdf/2609.09421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/76dsm4tk7m2v4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09421"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Induced random mixed states are symmetric Dirichlet mixtures",
  "title_text": "Induced random mixed states are symmetric Dirichlet mixtures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/76dsm4tk7m2v4",
  "venue": "arXiv",
  "versions": []
}