Relative entropy equals bulk relative entropy
Abstract
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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 June 2016
 DOI:
 10.1007/JHEP06(2016)004
 arXiv:
 arXiv:1512.06431
 Bibcode:
 2016JHEP...06..004J
 Keywords:

 AdSCFT Correspondence;
 1/N Expansion;
 Models of Quantum Gravity;
 Field Theories in Higher Dimensions;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 23 pages, 3 figures