  In the context of relating AdS/CFT to quantum information theory, we propose
a holographic dual of 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 subregion in the boundary we
show that this is related to a particularly regularized volume enclosed by the
Ryu-Takayanagi surface. We further argue that the quantum correction to the
proposed Fisher information metric is related to the quantum correction to the
boundary entanglement entropy. We discuss consequences of this connection.
