{
  "abstract": "A bipartite state is absolutely positive partial transpose (APPT) if it remains PPT under every global unitary transformation, and absolutely separable if it remains separable. For every qutrit--qudit system $\\mathbb{C}^3\\otimes\\mathbb{C}^n$, $n\\ge3$, we prove that the maximum purity is the same for absolutely separable and APPT states and equals $\\max\\{(3n+8)/(3n+2)^2,\\,3/(8n)\\}$. The maximizing ordered spectrum is unique and contains exactly two distinct eigenvalues: the larger one has multiplicity one for $3\\le n\\le8$ and multiplicity $n$ for $n\\ge9$. We also derive, in terms of the purity, an upper bound on the minimum partial-transpose eigenvalue achievable by global unitary transformations, and characterize all states for which the bound is attained. These results confirm the inscribed-polytope purity conjecture of Ahiable, Kothakonda, and Winter for all qutrit--qudit systems. They also give a lower bound, sharp over explicit purity ranges, on the global depolarizing noise needed for absolute separability or APPT.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01306",
  "author_total": 1,
  "authors": [
    {
      "name": "Anh T. Tran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hft83y9akk1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01306",
  "fulltext_url": null,
  "id": "5hft83y9akk1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01306",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01306",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hft83y9akk1q.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.01306",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01306"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Maximum purity of absolutely separable and absolutely PPT states in qutrit--qudit systems",
  "title_text": "Maximum purity of absolutely separable and absolutely PPT states in qutrit--qudit systems",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/5hft83y9akk1q",
  "venue": "arXiv",
  "versions": []
}