Nielsen's Theorem on characterizing pure state transformations

The Quantum Information Processing Reading (QIP) Seminar is an informal forum on QIP, organized by members of the Ctools group "qIP Reading Group" , which is open to the U-M community.
Suppose Alice and Bob start with a shared entangled state
|\phi>, what are the states |\psi> that they can obtain
through local quantum operations and classical communication?
Nielsen gave an elegant answer to this question by proving
that the set of |\psi> is precisely those whose vector of
Schmidt coefficients is *majorized* by that of |\phi>.
In this talk I will review this theorem, and discuss open
problems.