Remarks on on Kim's Strong Subadditivity Matrix Inequality: Extensions   and Equality Conditions
  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. 
Mary Beth Ruskai
quant-ph math-ph math.MP