Conditions for manipulation of a set of entangled pure states
  We derive a sufficient condition for a set of pure states, each entangled in two remote $N$-dimensional systems, to be transformable to $k$-dimensional-subspace equivalent entangled states ($k\leq N$) by same local operations and classical communication. If $k=N$, the condition is also necessary. This condition reveals the function of the relative marginal density operators of the entangled states in the entanglement manipulation without sufficient information of the initial states. 
Chuan-Wei Zhang, Chuan-Feng Li, and Guang-Can Guo (University of   Science and Technology of China)