Relative entropy equals bulk relative entropy. (English) Zbl 1388.83268
Summary: 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.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 83E30 | String and superstring theories in gravitational theory |
| 81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
| 94A17 | Measures of information, entropy |
Keywords:
AdS-CFT correspondence; \(1/N\) expansion; models of quantum gravity; field theories in higher dimensionsReferences:
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