ar X iv : q ua nt - p h / 01 03 15 8 v 3 5 J ul 2 00 1 More Is Not Necessarily Easier

We consider pure bipartite states shared by Alice and Bob. Let A and B be the labels of their respective quantum systems, each with d dimensions. Suppose Alice and Bob want to transform a state |ψ〉 to another state |φ〉. They each have complete classical descriptions of the states, but they can only perform Local quantum Operations and Classical Communication (LOCC) [1]. The transformation can be performed under many scenarios. The final state can be exactly or approximately the desired output, and the transformation can work deterministically or with certain probability. It is also possible to consider converting between an asymptotically large numbers of two different states.