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This paper will address the question of the distillation of entanglement froma finite number of multi-partite mixed states. It is shown that if one candistill 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 allcopies such that the projection of $\sigma_{ABC...}^{\otimes n}$ onto thesubspace is a pure entangled state. We also show that the purification ofentanglement or distillation of entanglement can be carried out by local jointprojective measurements with the help of classical communication and localgeneral positive operator valued measurements on a single particle, inprinciple. Finally we discuss experimental realizability of the entanglementpurification.Comment: to appear in PR

Distilling multipartite pure states from a finite number of copies of multipartite mixed states