{
  "abstract": "Absolutely positive partial transpose (APPT) states, which remain PPT under every global unitary, provide a spectral relaxation of absolutely separable states, which remain separable under every such transformation. Despite substantial progress, whether these two notions coincide beyond qubit-qudit systems remains unresolved, motivating the study of structured state families in which the APPT spectral constraints and separability can be analyzed exactly. We study this problem for Bell-diagonal states in two settings: the standard two-qutrit Weyl-Heisenberg basis and the two-ququart lattice basis generated by two-qubit Pauli operators. In the two-qutrit case, we show that a linearized necessary condition for APPT defines a polytope of spectra in which every associated Weyl-Heisenberg Bell-diagonal state admits an exact decomposition into explicitly separable states. This yields a separability criterion that applies to a region even larger than the APPT set itself. In the two-ququart lattice Bell-diagonal setting, we show that a state remains PPT under every permutation of its Bell coefficients if and only if its six largest Bell coefficients sum to at most 1/2, and we prove that all such states are separable. Equivalently, every entangled lattice Bell-diagonal state becomes NPT after a suitable coefficient permutation and is therefore not APPT. The proofs combine convex-polytope analysis, affine and symplectic orbit reductions, and exact rational decompositions into separable states supported on affine Lagrangian subsets. Our results rule out entangled APPT states in both Bell-diagonal families, and provide simple spectral inequalities as sufficient criteria for separability in both cases. Being basis-specific, however, they do not by themselves settle whether APPT and absolute separability coincide.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12000",
  "author_total": 2,
  "authors": [
    {
      "name": "Ayan Patra"
    },
    {
      "name": "Beatrix C. Hiesmayr"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3h6c5eg36ccne.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12000",
  "fulltext_url": null,
  "id": "3h6c5eg36ccne",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12000",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7221198008",
  "pdf_url": "https://arxiv.org/pdf/2610.12000",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3h6c5eg36ccne.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12000",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12000"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "On the separability of Bell-diagonal states with absolutely positive partial transposition",
  "title_text": "On the separability of Bell-diagonal states with absolutely positive partial transposition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/3h6c5eg36ccne",
  "venue": "arXiv",
  "versions": []
}