Correction to: Ruminations on matrix convexity and the strong subadditivity of quantum entropy

We correct here a mistake which is present in Eq. (5.7) of our paper [1].The error has only a minor local effect on the streamlined derivation of SSA presented there.However, the correction is of independent interest, as it leads to a decomposition of the quantum mutual information of a composite system into a sum of two terms, one of a distinctly quantum nature and another expressing a purely classical correlation effect.