Relative entropy equals bulk relative entropy
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.
 Authors:

^{[1]};
^{[2]};
^{[3]};
^{[4]}
 Harvard Univ., Cambridge, MA (United States). Center for Fundamental Laws of Nature
 Princeton Univ., NJ (United States)
 Inst. for Advanced Study, Princeton, NJ (United States)
 Kavli Inst. for Theoretical Physics, Santa Barbara, CA (United States); Univ. of British Columbia, Vancouver, BC (Canada). Dept. of Physics and Astronomy
 Publication Date:
 Grant/Contract Number:
 SC0009988; PHY1352084; PHY1314198; PHY1125915; 376206
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 6; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Research Org:
 Inst. for Advanced Study, Princeton, NJ (United States)
 Sponsoring Org:
 USDOE; National Science Foundation (NSF); Natural Sciences and Engineering Research Council of Canada (NSERC); Simons Foundation
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdSCFT Correspondence; 1/N Expansion, Models of Quantum Gravity; Field Theories in Higher Dimensions
 OSTI Identifier:
 1327000
Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, and Suh, S. Josephine. Relative entropy equals bulk relative entropy. United States: N. p.,
Web. doi:10.1007/JHEP06(2016)004.
Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, & Suh, S. Josephine. Relative entropy equals bulk relative entropy. United States. doi:10.1007/JHEP06(2016)004.
Jafferis, Daniel L., Lewkowycz, Aitor, Maldacena, Juan, and Suh, S. Josephine. 2016.
"Relative entropy equals bulk relative entropy". United States.
doi:10.1007/JHEP06(2016)004. https://www.osti.gov/servlets/purl/1327000.
@article{osti_1327000,
title = {Relative entropy equals bulk relative entropy},
author = {Jafferis, Daniel L. and Lewkowycz, Aitor and Maldacena, Juan and Suh, S. Josephine},
abstractNote = {We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.},
doi = {10.1007/JHEP06(2016)004},
journal = {Journal of High Energy Physics (Online)},
number = 6,
volume = 2016,
place = {United States},
year = {2016},
month = {6}
}