  The entanglement of the coupled massive scalar field in the spacetime of a
Garfinkle-Horowitz-Strominger(GHS) dilaton black hole has been investigated. It
is found that the entanglement does not depend on the mass of the particle and
the coupling between the scalar field and the gravitational field, but it
decreases as the dilaton parameter $D$ increases. It is interesting to note
that in the limit of $D\to M$, corresponding to the case of an extreme black
hole, the state has no longer distillable entanglement for any state parameter
$\alpha$, but the mutual information equals to a nonvanishing minimum value,
which indicates that the total correlations consist of classical correlations
plus bound entanglement in this limit.
