  We give an upper bound of the relative entanglement entropy of the ground
state of a massive Dirac-Majorana field across two widely separated regions $A$
and $B$ in a static slice of an ultrastatic Lorentzian spacetime. Our bound
decays exponentially in $dist (A, B)$, at a rate set by the Compton wavelength
and the spatial scalar curvature. The physical interpretation our result is
that, on a manifold with positive spatial scalar curvature, one cannot use the
entanglement of the vacuum state to teleport one classical bit from $A$ to $B$
if their distance is of the order of the maximum of the curvature radius and
the Compton wave length or greater.
