The connected wedge theorem and its consequences
Abstract In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2022)153 |
| _version_ | 1827985324011159552 |
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| author | Alex May Jonathan Sorce Beni Yoshida |
| author_facet | Alex May Jonathan Sorce Beni Yoshida |
| author_sort | Alex May |
| collection | DOAJ |
| description | Abstract In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in [3]. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions. |
| first_indexed | 2024-04-09T23:13:05Z |
| format | Article |
| id | doaj.art-684b48ae529345648561446e8cdb5e44 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:13:05Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-684b48ae529345648561446e8cdb5e442023-03-22T10:14:46ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221116510.1007/JHEP11(2022)153The connected wedge theorem and its consequencesAlex May0Jonathan Sorce1Beni Yoshida2Stanford Institute for Theoretical Physics, Stanford UniversityStanford Institute for Theoretical Physics, Stanford UniversityPerimeter Institute for Theoretical PhysicsAbstract In the AdS/CFT correspondence, bulk causal structure has consequences for boundary entanglement. In quantum information science, causal structures can be replaced by distributed entanglement for the purposes of information processing. In this work, we deepen the understanding of both of these statements, and their relationship, with a number of new results. Centrally, we present and prove a new theorem, the n-to-n connected wedge theorem, which considers n input and n output locations at the boundary of an asymptotically AdS2+1 spacetime described by AdS/CFT. When a sufficiently strong set of causal connections exists among these points in the bulk, a set of n associated regions in the boundary will have extensive-in-N mutual information across any bipartition of the regions. The proof holds in three bulk dimensions for classical spacetimes satisfying the null curvature condition and for semiclassical spacetimes satisfying standard conjectures. The n-to-n connected wedge theorem gives a precise example of how causal connections in a bulk state can emerge from large-N entanglement features of its boundary dual. It also has consequences for quantum information theory: it reveals one pattern of entanglement which is sufficient for information processing in a particular class of causal networks. We argue this pattern is also necessary, and give an AdS/CFT inspired protocol for information processing in this setting. Our theorem generalizes the 2-to-2 connected wedge theorem proven in [3]. We also correct some errors in the proof presented there, in particular a false claim that existing proof techniques work above three bulk dimensions.https://doi.org/10.1007/JHEP11(2022)153AdS-CFT CorrespondenceClassical Theories of GravityField Theories in Lower DimensionsModels of Quantum Gravity |
| spellingShingle | Alex May Jonathan Sorce Beni Yoshida The connected wedge theorem and its consequences Journal of High Energy Physics AdS-CFT Correspondence Classical Theories of Gravity Field Theories in Lower Dimensions Models of Quantum Gravity |
| title | The connected wedge theorem and its consequences |
| title_full | The connected wedge theorem and its consequences |
| title_fullStr | The connected wedge theorem and its consequences |
| title_full_unstemmed | The connected wedge theorem and its consequences |
| title_short | The connected wedge theorem and its consequences |
| title_sort | connected wedge theorem and its consequences |
| topic | AdS-CFT Correspondence Classical Theories of Gravity Field Theories in Lower Dimensions Models of Quantum Gravity |
| url | https://doi.org/10.1007/JHEP11(2022)153 |
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