{"ID":23523540,"CreatedAt":"2026-09-18T02:58:45.531918055Z","UpdatedAt":"2026-09-18T02:58:45.531918055Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19267","arxiv_id":"2609.19267","title":"Algebraic Complexity and Black Hole Complementarity","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.","short_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 th...","url_abs":"https://arxiv.org/abs/2609.19267","url_pdf":"https://arxiv.org/pdf/2609.19267v1","authors":"[\"Aude Corbeel\",\"Jingxin Tu\",\"Pim van den Heuvel\",\"Jeremy van der Heijden\",\"Erik Verlinde\"]","published":"2026-09-16T18:00:03Z","proceeding":"hep-th","tasks":"[\"hep-th\"]","methods":"[]","has_code":false}