  Extending our previous work, we study the relative entropy between the
reduced density matrices obtained from globally excited states in conformal
field theories of arbitrary dimensions. We find a general formula in the small
subsystem size limit. When one of the states is the vacuum of the CFT, our
result matches with the holographic entanglement entropy computations in the
corresponding bulk geometries, including AdS black branes. We also discuss the
first asymmetric part of the relative entropy and comment on some implications
of the results on the distinguishability of black hole microstates in AdS/CFT.
