  Known entanglement purification protocols for mixed states use collective
measurements on several copies of the state in order to increase the
entanglement of some of them. We address the question of whether it is possible
to purify the entanglement of a state by processing each copy separately. While
this is possible for pure states, we show that this is impossible, in general,
for mixed states. The importance of this result both conceptually and for
experimental realization of purification is discussed. We also give explicit
invariants of an entangled state of two qubits under local actions and
classical communication.
