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Extending our previous work, we study the relative entropy between thereduced density matrices obtained from globally excited states in conformalfield theories of arbitrary dimensions. We find a general formula in the smallsubsystem size limit. When one of the states is the vacuum of the CFT, ourresult matches with the holographic entanglement entropy computations in thecorresponding bulk geometries, including AdS black branes. We also discuss thefirst asymmetric part of the relative entropy and comment on some implicationsof the results on the distinguishability of black hole microstates in AdS/CFT.

Relative entropy of excited states in conformal field theories of arbitrary dimensions