{
  "abstract": "The entanglement of purification $E_P$, introduced by Terhal, Horodecki, Leung, and DiVincenzo in 2002, measures the total correlations of a bipartite state by the entanglement needed to purify it; whether it is additive on tensor powers has been open since its introduction. In 2012 Chen and Winter argued \"beyond reasonable doubt\", from numerical evidence, that the two-qubit Werner state at singlet fraction $f = 1/200$ is a counterexample, and explicitly left a completely rigorous proof to future work. To our knowledge we give the first rigorous proof: for this state $W$, $E_P^\\infty(W) \\le 0.9663\\ldots < 97/100 < E_P(W)$, hence the entanglement of purification is strictly nonadditive at some finite tensor power. The lower bound is a finite certificate: analytic reductions send the Schmidt spectrum of every purification in the complete complex Stiefel domain to a point satisfying explicit necessary inequalities in a three-dimensional box, and an exact-rational subdivision of that box has 25,383 leaves, each of which either excludes nonphysical points or proves the entropy bound. The upper bound combines an exact symmetric-support endpoint, an explicit feasible isometry, and a convexity theorem for the regularized quantity, closed by two directed rational logarithm certificates. Every computer-assisted certificate reduces to integer comparisons; a dependency-free program verifies all of them from the supplementary artifact.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29539",
  "author_total": 1,
  "authors": [
    {
      "name": "Artus Krohn-Grimberghe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9pnrhpczv5290.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29539",
  "fulltext_url": null,
  "id": "9pnrhpczv5290",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29539",
  "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": "W7214321074",
  "pdf_url": "https://arxiv.org/pdf/2609.29539",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9pnrhpczv5290.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.29539",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29539"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The entanglement of purification is not additive",
  "title_text": "The entanglement of purification is not additive",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/9pnrhpczv5290",
  "venue": "arXiv",
  "versions": []
}