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On the separability of Bell-diagonal states with absolutely positive partial transposition — arXiv:2610.12000

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.12000
License (as archived): CC0-1.0
Archived: 2026-10-09T06:39:12.719Z
SHA-256 of the archived text: 87c704e593679b1cb95325b915d1728af4098816e967b1ea81bd0dddd6665fa2
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How to cite

On the separability of Bell-diagonal states with absolutely positive partial transposition — arXiv:2610.12000 — arXiv (en), https://arxiv.org/abs/2610.12000 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7fbef4417cc7 (Metraipolis archive dc_7fbef4417cc7, sha256 87c704e593679b1cb95325b915d1728af4098816e967b1ea81bd0dddd6665fa2)

BibTeX

@misc{dc7fbef4417cc7,
  title = {On the separability of Bell-diagonal states with absolutely positive partial transposition — arXiv:2610.12000},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.12000},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7fbef4417cc7; sha256 87c704e593679b1cb95325b915d1728af4098816e967b1ea81bd0dddd6665fa2},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.12000. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.12000 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-09T05:58:46.992Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).