  We study the entropy associated with the Janus interface in a 4$d$
$\mathcal{N}=2$ superconformal field theory. With the entropy defined as the
interface contribution to an entanglement entropy we show, under mild
assumptions, that the Janus interface entropy is proportional to the geometric
quantity called Calabi's diastasis on the space of $\mathcal{N}=2$ marginal
couplings, confirming an earlier conjecture by two of the authors and
generalizing a similar result in two dimensions. Our method is based on a CFT
consideration that makes use of the Casini-Huerta-Myers conformal map from the
flat space to the round sphere.
