发表机构
Institute for Theoretical Physics, University of Amsterdam; Department of Physics and Astronomy, University of British Columbia（阿姆斯特丹大学理论物理研究所; 不列颠哥伦比亚大学物理与天文学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过算子代数推广Yoshida-Kitaev协议，利用有限指标包含和Jones构造定义代数复杂性，以Jones-Kosaki指标度量，并实现黑洞互补性的代数描述。
AI 中文摘要
我们将Yoshida-Kitaev信息恢复协议推广为算子代数版本，该版本适用于任意类型的冯·诺依曼代数。该构造基于有限指标包含，以Jones基本构造和典范自同态为核心代数工具。与有限维量子比特描述不同，无限维理论展现出新的结构现象，这些现象在信息恢复中起着关键作用。特别是，日记信息通过与该包含相关的Pimsner-Popa基的选择以非局域方式表示。利用Jones投影满足的Temperley-Lieb关系，我们引入了计算复杂性的代数概念，并证明其自然由Jones-Kosaki指标度量。对于不可约深度为二的包含，我们证明信息传递由代数傅里叶变换实现。最后，我们讨论了该构造的潜在时空解释，包括以（非）等距嵌入方式出现的岛屿代数，以及黑洞互补性的算子代数实现。
英文摘要
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.
Comments40 pages + appendices, 11 figures
