When Catalysis is Useful for Probabilistic Entanglement Transformation
  We determine all $2\times 2$ quantum states that can serve as useful catalysts for a given probabilistic entanglement transformation, in the sense that they can increase the maximal transformation probability. When higher-dimensional catalysts are considered, a sufficient and necessary condition is derived under which a certain probabilistic transformation has useful catalysts. 
Yuan Feng, Runyao Duan, Mingsheng Ying