Relative entropy equals bulk relative entropy

Abstract

We consider the gravity dual of the modular Hamiltonian associated to a\ngeneral subregion of a boundary theory. We use it to argue that the relative\nentropy of nearby states is given by the relative entropy in the bulk, to\nleading order in the bulk gravitational coupling. We also argue that the\nboundary modular flow is dual to the bulk modular flow in the entanglement\nwedge, with implications for entanglement wedge reconstruction.\n