{
  "abstract": "The study of entanglement inevitably leads to the concept of regularization, where measures are evaluated on infinitely many copies of a state. Single-letter formulas try to make these asymptotic entanglement quantities accessible through a calculation on one copy of a state, but are rarely available. We introduce a decreasing hierarchy of computable upper bounds on the asymptotic relative entropy of entanglement with respect to positive-partial-transpose (PPT) states. The regularization of every fixed hierarchy level equals this asymptotic quantity. Additivity at any level therefore yields a single-letter formula, even when the usual one-copy relative entropy is nonadditive. We establish such additivity at the first nontrivial level for two broad multiparameter families, both containing all Werner states. The upper-bound construction also extends to sandwiched Renyi divergences. The hierarchy motivates $k$-multinegative states, a generalization of binegative states and the associated $k$-multinegativity, which gives explicit upper bounds on both the asymptotic relative entropy and exact PPT entanglement cost. We construct states which are $k$-multinegative at arbitrarily large depths $k$ that separate consecutive levels of the previously introduced entanglement-cost hierarchy, disproving its conjectured finite collapse. These results provide state-dependent single-letter formulas while identifying a limitation of universal finite-level characterizations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20698",
  "author_total": 5,
  "authors": [
    {
      "name": "Raphael Brinster"
    },
    {
      "name": "Tulja Varun Kondra"
    },
    {
      "name": "Hermann Kampermann"
    },
    {
      "name": "Dagmar Bruß"
    },
    {
      "name": "Nikolai Wyderka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bksf16ecrc3rn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20698",
  "fulltext_url": null,
  "id": "bksf16ecrc3rn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20698",
  "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": "W7213600104",
  "pdf_url": "https://arxiv.org/pdf/2609.20698",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bksf16ecrc3rn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.20698",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20698"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multinegativity and single-letter formulas for asymptotic entanglement",
  "title_text": "Multinegativity and single-letter formulas for asymptotic entanglement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/bksf16ecrc3rn",
  "venue": "arXiv",
  "versions": []
}