Free mutual information for two projections

The present paper provides a proof of $i^*( $\mathbb{C}$P+$\mathbb{C}$(I-P); $\mathbb{C}$Q+$\mathbb{C}$(I-Q) )=-\chi_{orb}(P,Q)$fortwoprojections$P,Q$ without any extra assumptions. An analytic approach is adopted to the proof, based on a subordination result for the liberation process of symmetries associated with $P,Q$.