Entanglement transformation between sets of bipartite pure quantum   states using local operations
  Alice and Bob are given an unknown initial state chosen from a set of pure quantum states. Their task is to transform the initial state to a corresponding final pure state using local operations only. We prove necessary and sufficient conditions on the existence of such a transformation. We also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states. 
H. F. Chau, Chi-Hang Fred Fung, Chi-Kwong Li, Edward Poon and   Nung-Sing Sze
quant-ph