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.
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BibTeX
@misc{corbeel2026algebraic,
title = {{Algebraic Complexity and Black Hole Complementarity}},
author = {Aude Corbeel and Jingxin Tu and Pim van den Heuvel and Jeremy van der Heijden and Erik Verlinde},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19267},
eprint = {2609.19267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19267},
}
RIS
TY - UNPB
TI - Algebraic Complexity and Black Hole Complementarity
AU - Aude Corbeel
AU - Jingxin Tu
AU - Pim van den Heuvel
AU - Jeremy van der Heijden
AU - Erik Verlinde
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19267
UR - https://arxiv.org/abs/2609.19267
AB - 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.
ER -