  This paper gives concrete examples to exhibit how to use the replica trick to
calculate the quantum (quasi-)distances holographically. First, we consider the
fidelity and relative entropy between thermal states that are dual to the
Schwarzschild-AdS black holes. Then we generalize our method into the RN-AdS
black holes by adding a U(1) gauge field. We also investigate the fidelity
between states excited by scalar operator in probe limit. In this case, it is
surprising that the fidelity in standard quantization will suffer from new UV
divergence though the usual holographic renormalization has been applied. We
call for deep understanding for such divergence in the future. We also discover
a holographic method to check whether the density matrices of two holographic
states are commutative.
