  In the framework of Algebraic Quantum Field Theory, several operator
algebraic notions of entanglement entropy can be associated to a couple of
causally disjoint and distant spacetime regions $\mathcal{S}_A$ and
$\mathcal{S}_B$. In this work, we show that the mutual information is finite in
any local QFT verifying a modular $p$-nuclearity condition for some $0 < p <1$.
A similar result is proved for another recently studied entanglement measure.
Furthermore, if we assume conformal covariance then by comparison with other
entanglement measures we can state that the mutual information satisfies lower
bounds of area law type when the distance between $\mathcal{S}_A$ and
$\mathcal{S}_B$ approaches to zero. As an application, in $1+1$-dimensional
integrable models with factorizing S-matrices, we study the asymptotic
behaviour of different entanglement measures as the distance between two
causally disjoint wedges diverges.
