  We propose a covariant scheme for measuring entanglement on general
hypersurfaces in relativistic quantum field theory. For that, we introduce an
auxiliary relativistic field, 'the discretizer', that by locally interacting
with the field along a hypersurface, fully swaps the field's and discretizer's
states. It is shown, that the discretizer can be used to effectively cut-off
the field's infinities, in a covariant fashion, and without having to introduce
a spatial lattice. This, in turn, provides us an efficient way to evaluate
entanglement between arbitrary regions on any hypersurface. As examples, we
study the entanglement between complementary and separated regions in 1+1
dimensions, for flat hypersurfaces in Minkowski space, for curved hypersurfaces
in Milne space, and for regions on hypersurfaces approaching null-surfaces. Our
results show that the entanglement between regions on arbitrary hypersurfaces
in 1+1 dimensions depends only on the space-time endpoints of the regions, and
not on the shape of the interior. Our results corroborate and extend previous
results for flat hypersurfaces.
