Entanglement wedge reconstruction using the Petz map
Abstract At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of hologr...
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SpringerOpen
2020-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2020)168 |
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| author | Chi-Fang Chen Geoffrey Penington Grant Salton |
| author_facet | Chi-Fang Chen Geoffrey Penington Grant Salton |
| author_sort | Chi-Fang Chen |
| collection | DOAJ |
| description | Abstract At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension — no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction. |
| format | Article |
| id | doaj-art-eebd89788ee14af5be40591160b42175 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-eebd89788ee14af5be40591160b421752025-02-09T12:06:39ZengSpringerOpenJournal of High Energy Physics1029-84792020-01-012020111410.1007/JHEP01(2020)168Entanglement wedge reconstruction using the Petz mapChi-Fang Chen0Geoffrey Penington1Grant Salton2Department of Physics, Stanford UniversityStanford Institute for Theoretical Physics, Stanford UniversityDepartment of Physics, Stanford UniversityAbstract At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension — no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.https://doi.org/10.1007/JHEP01(2020)168AdS-CFT Correspondence1/N ExpansionNonperturbative Effects |
| spellingShingle | Chi-Fang Chen Geoffrey Penington Grant Salton Entanglement wedge reconstruction using the Petz map Journal of High Energy Physics AdS-CFT Correspondence 1/N Expansion Nonperturbative Effects |
| title | Entanglement wedge reconstruction using the Petz map |
| title_full | Entanglement wedge reconstruction using the Petz map |
| title_fullStr | Entanglement wedge reconstruction using the Petz map |
| title_full_unstemmed | Entanglement wedge reconstruction using the Petz map |
| title_short | Entanglement wedge reconstruction using the Petz map |
| title_sort | entanglement wedge reconstruction using the petz map |
| topic | AdS-CFT Correspondence 1/N Expansion Nonperturbative Effects |
| url | https://doi.org/10.1007/JHEP01(2020)168 |
| work_keys_str_mv | AT chifangchen entanglementwedgereconstructionusingthepetzmap AT geoffreypenington entanglementwedgereconstructionusingthepetzmap AT grantsalton entanglementwedgereconstructionusingthepetzmap |