{
  "abstract": "We study the entanglement dynamics of two qutrits under collective dephasing for a family of states obtained by mixing a maximally entangled state that lives in the decoherence-free subspace with three nonstationary two-term states sharing a common amplitude ratio $r$. We obtain exact PPT and separability regions along the whole trajectory, a specialization of known results on cyclic sign invariant states, and we supply explicit certificates: a finite product decomposition, three fixed positive-map witnesses, and a closed realignment formula that detects every PPT-entangled state, so that no state is left undecided. The negativity is computed in closed form. It shows that the entanglement is time-invariant, positive and constant from the initial time although the state changes, exactly when the weight of the maximally entangled state exceeds the threshold $U_r=r/(1+r+r^2)$. To our knowledge, this is the first demonstration of time-invariant entanglement for qutrit--qutrit systems under collective dephasing. For smaller weights the entanglement decays and vanishes at a finite time: the state either becomes separable (entanglement sudden death) or, for $r\\neq1$ in an intermediate range, loses distillability suddenly and remains bound entangled at all later times. Every state with negative partial transpose is one-copy distillable by a fixed local projection. The same trajectories arise from the global dephasing map and from a correlated local random-unitary semigroup, although the two channels differ on product inputs. Exact rational benchmarks and embeddings of the Horodecki and Ha--Kye--Park families are provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04568",
  "author_total": 3,
  "authors": [
    {
      "name": "Wenlin Zhang"
    },
    {
      "name": "Mazhar Ali"
    },
    {
      "name": "Haobo Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5tr7wrt4pyh1s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04568",
  "fulltext_url": null,
  "id": "5tr7wrt4pyh1s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04568",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5tr7wrt4pyh1s.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04568"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Time-invariant negativity and persistent bound entanglement in a cyclic two-qutrit family",
  "title_text": "Time-invariant negativity and persistent bound entanglement in a cyclic two-qutrit family",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/5tr7wrt4pyh1s",
  "venue": "arXiv",
  "versions": []
}