  We describe recent work of Kim in arXiv:1210.5190 to show that operator
convex functions associated with quasi-entropies can be used to prove a large
class of new matrix inequalities in the tri-partite and bi-partite setting by
taking a judiciously chosen partial trace over all but one of the spaces. We
give some additional examples in both settings. Furthermore, we observe that
the equality conditions for all the new inequalities are essentially the same
as those for strong subadditivity.
