Learning the Alpha-bits of black holes
Abstract When the bulk geometry in AdS/CFT contains a black hole, boundary subregions may be sufficient to reconstruct certain bulk operators if and only if the black hole microstate is known, an example of state dependence. Reconstructions exist for any microstate, but no reconstruction works for a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2019)007 |
| _version_ | 1818602599008436224 |
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| author | Patrick Hayden Geoffrey Penington |
| author_facet | Patrick Hayden Geoffrey Penington |
| author_sort | Patrick Hayden |
| collection | DOAJ |
| description | Abstract When the bulk geometry in AdS/CFT contains a black hole, boundary subregions may be sufficient to reconstruct certain bulk operators if and only if the black hole microstate is known, an example of state dependence. Reconstructions exist for any microstate, but no reconstruction works for all microstates. We refine this dichotomy, demonstrating that the same boundary operator can often be used for large subspaces of black hole microstates, corresponding to a constant fraction α of the black hole entropy. In the Schrödinger picture, the boundary subregion encodes the α-bits (a concept from quantum information) of a bulk region containing the black hole and bounded by extremal surfaces. These results have important consequences for the structure of AdS/CFT and for quantum information. Firstly, they imply that the bulk reconstruction is necessarily only approximate and allow us to place non-perturbative lower bounds on the error when doing so. Second, they provide a simple and tractable limit in which the entanglement wedge is state dependent, but in a highly controlled way. Although the state dependence of operators comes from ordinary quantum error correction, there are clear connections to the Papadodimas-Raju proposal for understanding operators behind black hole horizons. In tensor network toy models of AdS/CFT, we see how state dependence arises from the bulk operator being ‘pushed’ through the black hole itself. Finally, we show that black holes provide the first ‘explicit’ examples of capacity-achieving α-bit codes. Unintuitively, Hawking radiation always reveals the α-bits of a black hole as soon as possible. In an appendix, we apply a result from the quantum information literature to prove that entanglement wedge reconstruction can be made exact to all orders in 1/N. |
| first_indexed | 2024-12-16T13:09:50Z |
| format | Article |
| id | doaj.art-0a729269df2f41a49ceb090293d7a423 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-16T13:09:50Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-0a729269df2f41a49ceb090293d7a4232022-12-21T22:30:38ZengSpringerOpenJournal of High Energy Physics1029-84792019-12-0120191215510.1007/JHEP12(2019)007Learning the Alpha-bits of black holesPatrick Hayden0Geoffrey Penington1Stanford Institute for Theoretical Physics, Stanford UniversityStanford Institute for Theoretical Physics, Stanford UniversityAbstract When the bulk geometry in AdS/CFT contains a black hole, boundary subregions may be sufficient to reconstruct certain bulk operators if and only if the black hole microstate is known, an example of state dependence. Reconstructions exist for any microstate, but no reconstruction works for all microstates. We refine this dichotomy, demonstrating that the same boundary operator can often be used for large subspaces of black hole microstates, corresponding to a constant fraction α of the black hole entropy. In the Schrödinger picture, the boundary subregion encodes the α-bits (a concept from quantum information) of a bulk region containing the black hole and bounded by extremal surfaces. These results have important consequences for the structure of AdS/CFT and for quantum information. Firstly, they imply that the bulk reconstruction is necessarily only approximate and allow us to place non-perturbative lower bounds on the error when doing so. Second, they provide a simple and tractable limit in which the entanglement wedge is state dependent, but in a highly controlled way. Although the state dependence of operators comes from ordinary quantum error correction, there are clear connections to the Papadodimas-Raju proposal for understanding operators behind black hole horizons. In tensor network toy models of AdS/CFT, we see how state dependence arises from the bulk operator being ‘pushed’ through the black hole itself. Finally, we show that black holes provide the first ‘explicit’ examples of capacity-achieving α-bit codes. Unintuitively, Hawking radiation always reveals the α-bits of a black hole as soon as possible. In an appendix, we apply a result from the quantum information literature to prove that entanglement wedge reconstruction can be made exact to all orders in 1/N.https://doi.org/10.1007/JHEP12(2019)007AdS-CFT CorrespondenceGauge-gravity correspondence |
| spellingShingle | Patrick Hayden Geoffrey Penington Learning the Alpha-bits of black holes Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence |
| title | Learning the Alpha-bits of black holes |
| title_full | Learning the Alpha-bits of black holes |
| title_fullStr | Learning the Alpha-bits of black holes |
| title_full_unstemmed | Learning the Alpha-bits of black holes |
| title_short | Learning the Alpha-bits of black holes |
| title_sort | learning the alpha bits of black holes |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence |
| url | https://doi.org/10.1007/JHEP12(2019)007 |
| work_keys_str_mv | AT patrickhayden learningthealphabitsofblackholes AT geoffreypenington learningthealphabitsofblackholes |