General and Optimal Scheme for Local Conversion of Pure States

We present general and optimal schemes for local conversion of pure states, via one specific example. First, we give the general solution of the doubly stochastic matrix. Then, we find the general and optimal positive-operator-valued measure (POVM) to realize the local conversion of pure states. Lastly, the physical realization of the POVM is discussed. We show that our scheme has a more general and better effect than other schemes.