  We introduce a series of quantities which characterizes a given local
operator in conformal field theories from the viewpoint of quantum
entanglement. It is defined by the increased amount of (Renyi) entanglement
entropy at late time for an excited state defined by acting the local operator
on the vacuum. We consider a conformal field theory on an infinite space and
take the subsystem in the definition of the entanglement entropy to be its
half. We calculate these quantities for a free massless scalar field theory in
2, 4 and 6 dimensions. We find that these results are interpreted in terms of
quantum entanglement of finite number states, including EPR states. They agree
with a heuristic picture of propagations of entangled particles.
