  This paper will address the question of the distillation of entanglement from
a finite number of multi-partite mixed states. It is shown that if one can
distill a pure entangled state from n copies of a mixed state $\sigma
_{ABC...}$ there must be at least a subspace in whole Hilbert space of the all
copies such that the projection of $\sigma_{ABC...}^{\otimes n}$ onto the
subspace is a pure entangled state. We also show that the purification of
entanglement or distillation of entanglement can be carried out by local joint
projective measurements with the help of classical communication and local
general positive operator valued measurements on a single particle, in
principle. Finally we discuss experimental realizability of the entanglement
purification.
