  We calculate Sorkin's spacetime entanglement entropy of a Gaussian scalar
field for complementary regions in the 2d cylinder spacetime and show that it
has the Calabrese-Cardy form. We find that the cut-off dependent term is
universal when we use a covariant UV cut-off. In addition, we show that the
relative size-dependent term exhibits complementarity. Its coefficient is
however not universal and depends on the choice of pure state. It asymptotes to
the universal form within a natural class of pure states.
