{
  "abstract": "We develop an operator algebraic generalization of the Yoshida-Kitaev information recovery protocol that applies to von Neumann algebras of arbitrary type. The construction is based on finite-index inclusions, with the Jones basic construction and canonical endomorphisms providing the central algebraic tools. Unlike the finite-dimensional qubit description, the infinite-dimensional theory exhibits new structural phenomena that play an essential role in information recovery. In particular, the diary information is represented non-locally by a choice of Pimsner-Popa basis associated with the inclusion. Exploiting the Temperley-Lieb relations satisfied by the Jones projections, we introduce an algebraic notion of computational complexity and show that it is naturally measured by the Jones-Kosaki index. For irreducible depth-two inclusions, we demonstrate that the information transfer is implemented by an algebraic Fourier transform. Finally, we discuss a potential spacetime interpretation of the construction, including the emergence of an island algebra in terms of (non-)isometric embeddings and an operator algebraic realization of black hole complementarity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19267",
  "author_total": 5,
  "authors": [
    {
      "name": "Aude Corbeel"
    },
    {
      "name": "Jingxin Tu"
    },
    {
      "name": "Pim van den Heuvel"
    },
    {
      "name": "Jeremy van der Heijden"
    },
    {
      "name": "Erik Verlinde"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/66zek409h20wh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19267",
  "fulltext_url": null,
  "id": "66zek409h20wh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19267",
  "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",
      "hep-th"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213584319",
  "pdf_url": "https://arxiv.org/pdf/2609.19267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/66zek409h20wh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2609.19267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19267"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Algebraic Complexity and Black Hole Complementarity",
  "title_text": "Algebraic Complexity and Black Hole Complementarity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/66zek409h20wh",
  "venue": "arXiv",
  "versions": []
}