Holographic inequalities and entanglement of purification
Abstract We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tri...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-03-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP03(2018)006 |
| _version_ | 1818443560830107648 |
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| author | Ning Bao Illan F. Halpern |
| author_facet | Ning Bao Illan F. Halpern |
| author_sort | Ning Bao |
| collection | DOAJ |
| description | Abstract We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications. |
| first_indexed | 2024-12-14T19:01:59Z |
| format | Article |
| id | doaj.art-b107e2e0d9794461acdcd4cf0cd21e3d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-14T19:01:59Z |
| publishDate | 2018-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-b107e2e0d9794461acdcd4cf0cd21e3d2022-12-21T22:50:56ZengSpringerOpenJournal of High Energy Physics1029-84792018-03-012018311710.1007/JHEP03(2018)006Holographic inequalities and entanglement of purificationNing Bao0Illan F. Halpern1Center for Theoretical Physics and Department of Physics, University of CaliforniaCenter for Theoretical Physics and Department of Physics, University of CaliforniaAbstract We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states. In addition, we use the cyclic entropy inequalities to derive a new holographic inequality for the entanglement wedge cross-section, and provide numerical evidence that the corresponding inequality for the entanglement of purification may be true in general. Finally, we use intuition from bit threads to extend the conjecture to holographic duals of suboptimal purifications.http://link.springer.com/article/10.1007/JHEP03(2018)006AdS-CFT CorrespondenceGauge-gravity correspondence |
| spellingShingle | Ning Bao Illan F. Halpern Holographic inequalities and entanglement of purification Journal of High Energy Physics AdS-CFT Correspondence Gauge-gravity correspondence |
| title | Holographic inequalities and entanglement of purification |
| title_full | Holographic inequalities and entanglement of purification |
| title_fullStr | Holographic inequalities and entanglement of purification |
| title_full_unstemmed | Holographic inequalities and entanglement of purification |
| title_short | Holographic inequalities and entanglement of purification |
| title_sort | holographic inequalities and entanglement of purification |
| topic | AdS-CFT Correspondence Gauge-gravity correspondence |
| url | http://link.springer.com/article/10.1007/JHEP03(2018)006 |
| work_keys_str_mv | AT ningbao holographicinequalitiesandentanglementofpurification AT illanfhalpern holographicinequalitiesandentanglementofpurification |