{
  "abstract": "Optimal approximate state conversion is a fundamental task in quantum resource theories, yet existing solutions are largely tailored to specific distinguishability measures and resource theories. We show that every optimal approximate-conversion problem in the three paradigmatic majorization-based quantum resource theories of non-uniformity, bipartite pure-state entanglement, and pure-state coherence reduces exactly to one of only four elementary taut-string constructions. This holds for problems generated by Schur-convex spectral distances and by a broad family of quantum divergences satisfying a natural reduction property with respect to the corresponding equivalence group. The resulting framework encompasses a broad class of physically relevant distinguishability measures, including the trace distance, all unitarily invariant norms, quantum relative entropy, maximal quantum $f$-divergences, and the $α$-$z$ Rényi relative entropies. The increment vector of the corresponding taut string completely determines both the optimal approximation error and a canonical optimal state. Our results establish a common geometric framework for approximate quantum resource conversion, revealing that a broad class of seemingly different optimization problems is governed by the same taut-string geometric principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28015",
  "author_total": 5,
  "authors": [
    {
      "name": "Franco Meroi"
    },
    {
      "name": "Cesar Massri"
    },
    {
      "name": "Marcelo Losada"
    },
    {
      "name": "Guido Bellomo"
    },
    {
      "name": "Gustavo Martin Bosyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/585p6qk39agjv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28015",
  "fulltext_url": null,
  "id": "585p6qk39agjv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28015",
  "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": "W7223149293",
  "pdf_url": "https://arxiv.org/pdf/2610.28015",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/585p6qk39agjv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.28015",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28015"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories",
  "title_text": "Optimal Approximate Quantum Conversion from a Taut-String Principle in Majorization-Based Resource Theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/585p6qk39agjv",
  "venue": "arXiv",
  "versions": []
}