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Purity maxima, absolute separability, and spectral volumes of absolutely PPT states — arXiv:2611.01492

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.01492
License (as archived): CC0-1.0
Archived: 2026-11-03T19:01:04.754Z
SHA-256 of the archived text: 8727eec2d47d4db016845cb96e830fc4dc5d8d3a04c40cd76343780a64185452
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How to cite

Purity maxima, absolute separability, and spectral volumes of absolutely PPT states — arXiv:2611.01492 — arXiv (en), https://arxiv.org/abs/2611.01492 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_caea017cd8fe (Metraipolis archive dc_caea017cd8fe, sha256 8727eec2d47d4db016845cb96e830fc4dc5d8d3a04c40cd76343780a64185452)

BibTeX

@misc{dccaea017cd8fe,
  title = {Purity maxima, absolute separability, and spectral volumes of absolutely PPT states — arXiv:2611.01492},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.01492},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_caea017cd8fe; sha256 8727eec2d47d4db016845cb96e830fc4dc5d8d3a04c40cd76343780a64185452},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.01492. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For $m\otimes n$ systems with $n\ge m\ge3$, we determine the exact maximum purity of absolutely positive partial transpose (APPT) states and the unique maximizing ordered spectrum when $n\ge2m^2-4$ for even $m$ or $n\ge2m^2-m-4$ for odd $m$. Under these dimension assumptions, absolutely separable states have the same maximum purity, attained at the same unique ordered spectrum. The proof uses an outer polytope defined by two linear head--tail inequalities, each comparing a sum of the largest eigenvalues with a sum of the smallest. Under explicit multiplicity assumptions, we derive an exact matrix criterion for APPT membership of full-rank spectra with three distinct eigenvalues. For every $m\ge10$, this criterion gives explicit APPT boundary spectra at $n=4m-2$ and $n=4m$ that disprove both cases of the maximum purity conjecture of Ahiable, Kothakonda, and Winter. We also determine the exact completely absolutely separable (CAS) purity maximum and its unique maximizing ordered spectrum in every bipartite dimension. We prove that the inner APPT polytope consists entirely of absolutely separable spectra. The resulting linear sufficient condition for absolute separability strictly improves the reduction-map and eigenvalue-ratio tests. Finally, we compute the exact relative volumes of the CAS set and an outer polytope defined by a single head--tail inequality. Under the uniform measure on spectra, the CAS, absolutely separable, and APPT volumes have the same asymptotic order $\sqrt n\,e^{-\kappa_m n}$ for every fixed $m\ge2$, with explicit $\kappa_m>0$.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2611.01492 — 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 2026-11-03T18:19:52.794Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).