{
  "abstract": "Entanglement of purification is a fundamental measure of total correlations whose additivity remains unresolved. We study its additivity for classical states on two qubits at different Rényi orders. For every $α\\in[0,1)$, we prove nonadditivity within this family, witnessed by two copies of a single state. We first solve the one-copy optimization exactly for the entire family at every Rényi order. We then restrict the two-copy optimization to a natural finite set of purifications and exhibit one whose entropy is strictly below the product value. In contrast, for $α\\in[2,\\infty]$ we prove additivity under tensor products within this family. The interval $α\\in[1,2)$, including the von Neumann case $α=1$, remains open, and we conjecture additivity there throughout the same family.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28897",
  "author_total": 2,
  "authors": [
    {
      "name": "Amir-Reza Negari"
    },
    {
      "name": "Zahra Baghali Khanian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e14p49xxkf5vj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28897",
  "fulltext_url": null,
  "id": "e14p49xxkf5vj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28897",
  "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",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7204911500",
  "pdf_url": "https://arxiv.org/pdf/2608.28897",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e14p49xxkf5vj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.28897",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28897"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rényi Entanglement of Purification Is Non-additive",
  "title_text": "Rényi Entanglement of Purification Is Non-additive",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/e14p49xxkf5vj",
  "venue": "arXiv",
  "versions": []
}