  In this paper, we use the replica approach to study the R\'enyi entropy $S_L$
of generic locally excited states in (1+1)D CFTs, which are constructed from
the insertion of multiple product of local primary operators on vacuum.
Alternatively, one can calculate the R\'enyi entropy $S_R$ corresponding to the
same states using Schmidt decomposition and operator product expansion, which
reduces the multiple product of local primary operators to linear combination
of operators. The equivalence $S_L=S_R$ translates into an identity in terms of
the $F$ symbols and quantum dimensions for rational CFT, and the latter can be
proved algebraically. This, along with a series of papers, gives a complete
picture of how the quantum information quantities and the intrinsic structure
of (1+1)D CFTs are consistently related.
