{
  "abstract": "We prove that the von Neumann entanglement of purification is nonadditive. For two-qubit Werner states $W(f)$ with singlet weight $1/64\\le f\\le1/4$, we show that canonical purification is globally optimal: its entanglement, also known as reflected entropy, gives the exact entanglement of purification. In contrast, the regularized entanglement of purification lies strictly below the reflected entropy for $0<f<f_\\ast$, where $f_\\ast\\approx0.017$. Together, these results establish nonadditivity throughout $1/64\\le f<f_\\ast$. Our canonical-optimality proof generalizes the proof in [1], which established Rényi nonadditivity for $0\\leα<1$ using classical two-qubit states. We thus resolve the additivity question at $α=1$. Remarkably, nonadditivity is again witnessed by separable states and no entanglement in the underlying states is required.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03630",
  "author_total": 2,
  "authors": [
    {
      "name": "Zahra Baghali Khanian"
    },
    {
      "name": "Amir-Reza Negari"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1krb616gc0hca.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03630",
  "fulltext_url": null,
  "id": "1krb616gc0hca",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03630",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.03630",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1krb616gc0hca.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03630",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03630"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Entanglement of purification for Werner states: canonical purification and nonadditivity",
  "title_text": "Entanglement of purification for Werner states: canonical purification and nonadditivity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/1krb616gc0hca",
  "venue": "arXiv",
  "versions": []
}