Mutual information superadditivity and unitarity bounds
Abstract We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These uni...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2021)046 |
| _version_ | 1819094452122157056 |
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| author | Horacio Casini Eduardo Testé Gonzalo Torroba |
| author_facet | Horacio Casini Eduardo Testé Gonzalo Torroba |
| author_sort | Horacio Casini |
| collection | DOAJ |
| description | Abstract We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones. |
| first_indexed | 2024-12-21T23:27:38Z |
| format | Article |
| id | doaj.art-5d01be934eed4711ac95f7643096898f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T23:27:38Z |
| publishDate | 2021-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5d01be934eed4711ac95f7643096898f2022-12-21T18:46:34ZengSpringerOpenJournal of High Energy Physics1029-84792021-09-012021913810.1007/JHEP09(2021)046Mutual information superadditivity and unitarity boundsHoracio Casini0Eduardo Testé1Gonzalo Torroba2Centro Atómico Bariloche and CONICETDepartment of Physics, University of CaliforniaCentro Atómico Bariloche and CONICETAbstract We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.https://doi.org/10.1007/JHEP09(2021)046Conformal Field TheoryRenormalization Group |
| spellingShingle | Horacio Casini Eduardo Testé Gonzalo Torroba Mutual information superadditivity and unitarity bounds Journal of High Energy Physics Conformal Field Theory Renormalization Group |
| title | Mutual information superadditivity and unitarity bounds |
| title_full | Mutual information superadditivity and unitarity bounds |
| title_fullStr | Mutual information superadditivity and unitarity bounds |
| title_full_unstemmed | Mutual information superadditivity and unitarity bounds |
| title_short | Mutual information superadditivity and unitarity bounds |
| title_sort | mutual information superadditivity and unitarity bounds |
| topic | Conformal Field Theory Renormalization Group |
| url | https://doi.org/10.1007/JHEP09(2021)046 |
| work_keys_str_mv | AT horaciocasini mutualinformationsuperadditivityandunitaritybounds AT eduardoteste mutualinformationsuperadditivityandunitaritybounds AT gonzalotorroba mutualinformationsuperadditivityandunitaritybounds |