  The present notes provide a proof of
$i^*(\mathbb{C}P+\mathbb{C}(I-P)\,;\mathbb{C}Q+\mathbb{C}(I-Q)) =
-\chi_\mathrm{orb}(P,Q)$ for any pair of projections $P,Q$ with
$\tau(P)=\tau(Q)=1/2$. The proof includes new extra observations, such as a
subordination result in terms of Loewner equations. A study of the general case
is also given.
