An Operator Algebraic Approach To Black Hole Information
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913454262059008 |
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| author | van der Heijden, Jeremy Verlinde, Erik |
| author_facet | van der Heijden, Jeremy Verlinde, Erik |
| contents | We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the information puzzle that is well-posed in the $G\to 0$ limit. We then give a description of the information recovery protocol in terms of von Neumann algebras using elements of the Jones index theory of type II$_1$ subfactors. The subsequent evaporation and recovery steps are represented by Jones's basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level "translation = teleportation". |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Operator Algebraic Approach To Black Hole Information van der Heijden, Jeremy Verlinde, Erik High Energy Physics - Theory We present an operator algebraic perspective on the black hole information problem. For a black hole after Page time that is entangled with the early radiation we formulate a version of the information puzzle that is well-posed in the $G\to 0$ limit. We then give a description of the information recovery protocol in terms of von Neumann algebras using elements of the Jones index theory of type II$_1$ subfactors. The subsequent evaporation and recovery steps are represented by Jones's basic construction, and an operation called the canonical shift. A central element in our description is the Jones projection, which leads to an entanglement swap and implements an operator algebraic version of a quantum teleportation protocol. These aspects are further elaborated on in a microscopic model based on type I algebras. Finally, we argue that in the emergent type III algebra the canonical shift may be interpreted as a spacetime translation and, hence, that at the microscopic level "translation = teleportation". |
| title | An Operator Algebraic Approach To Black Hole Information |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.00071 |