  This is an expanded version of the short report arXiv:1401.0539, where we
stud- ied the (Renyi) entanglement entropies for the excited state defined by
acting a given local operator on the ground state. We introduced the (Renyi)
entanglement entropies of given local operators which measure the degrees of
freedom of local operators and characterize them in conformal field theories
from the viewpoint of quantum entanglement. In present paper, we explain how to
compute them in free massless scalar field theories and we also investigate
their time evolution. The results are interpreted in terms of relativistic
propagation of an entangled pair. The main new results which we acquire in the
present paper are as follows. Firstly, we provide an explanation which shows
that the (Renyi) entanglement entropies of a specific operator are given by
(Renyi) entanglement entropies of binomial distribution by the replica method.
That operator is constructed of only scalar field. Secondly, we found the sum
rule which (Renyi) entanglement entropies of those local operators obey. Those
local operators are located separately. Moreover we argue that (Renyi)
entanglement entropies of specific operators in conformal field theories are
given by (Renyi) entanglement entropies of binomial distribution. These
specific operators are constructed of single-species operator. We also argue
that general operators obey the sum rule which we mentioned above.
