  We mainly study the R\'enyi entropy and entanglement entropy of the states
locally excited by the descendent operators in two dimensional conformal field
theories (CFTs). In rational CFTs, we prove that the increase of entanglement
entropy and R\'enyi entropy for a class of descendent operators, which are
generated by $\cal{L}^{(-)}\bar{\cal{L}}^{(-)}$ onto the primary operator,
always coincide with the logarithmic of quantum dimension of the corresponding
primary operator. That means the R\'enyi entropy and entanglement entropy for
these descendent operators are the same as the ones of their corresponding
primary operator. For 2D rational CFTs with a boundary, we confirm that the
R\'enyi entropy always coincides with the logarithmic of quantum dimension of
the primary operator during some periods of the evolution. Furthermore, we
consider more general descendent operators generated by $\sum_{}
d_{\{n_i\}\{n_j\}}(\prod_{i} L_{-n_i}\prod_{j}{\bar L}_{-n_j})$ on the primary
operator. For these operators, the entanglement entropy and R\'enyi entropy get
additional corrections, as the mixing of holomorphic and anti-holomorphic
Virasoro generators enhance the entanglement. Finally, we employ perturbative
CFT techniques to evaluate the R\'enyi entropy of the excited operators in
deformed CFT. The R\'enyi and entanglement entropies are increased, and get
contributions not only from local excited operators but also from global
deformation of the theory.
