  We develop the computational method of entanglement entropy based on the idea
that $Tr\rho_{\Omega}^n$ is written as the expectation value of the local
operator, where $\rho_{\Omega}$ is a density matrix of the subsystem $\Omega$.
We apply it to consider the mutual Renyi information
$I^{(n)}(A,B)=S^{(n)}_A+S^{(n)}_B-S^{(n)}_{A\cup B}$ of disjoint compact
spatial regions $A$ and $B$ in the locally excited states defined by acting the
local operators at $A$ and $B$ on the vacuum of a $(d+1)$-dimensional field
theory, in the limit when the separation $r$ between $A$ and $B$ is much
greater than their sizes $R_{A,B}$. For the general QFT which has a mass gap,
we compute $I^{(n)}(A,B)$ explicitly and find that this result is interpreted
in terms of an entangled state in quantum mechanics. For a free massless scalar
field, we show that for some classes of excited states,
$I^{(n)}(A,B)-I^{(n)}(A,B)|_{r \rightarrow \infty} =C^{(n)}_{AB}/r^{\alpha
(d-1)}$ where $\alpha=1$ or 2 which is determined by the property of the local
operators under the transformation $\phi \rightarrow -\phi$ and $\alpha=2$ for
the vacuum state. We give a method to compute $C^{(2)}_{AB}$ systematically.
