Entropy measures and catalysis of bipartite quantum state transformations

Given probability vectors x and y, necessary and sufficient conditions are given for the existence of a probability vector z such that xominusz is majorized by yominusz. This is of interest because the "catalytic majorization" relation is known to be useful in classifying which transformations of jointly held pure quantum states are possible using local operations and classical communication when an additional jointly held state may be specified to facilitate the transformation without being consumed