Connecting Fisher information to bulk entanglement in holography
ABSTRACT :
In the context of relating AdS/CFT to quantum information theory, we propose a holographic dual of the Fisher information metric for mixed states in the boundary field theory. This amounts to a holographic measure for the distance between two mixed quantum states. For a spherical sub-region, we study various excited states in the boundary and show that this is related to a particularly regularized volume enclosed by the corresponding Ryu-Takayanagi surfaces. We discuss consequences of this connection at order by order in boundary perturbation theory and finally, some ongoing progress along this direction.