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

This paper addresses the question of the distillation of entanglement from a finite number of multipartite mixed states. It is shown that, if one can distill a pure entangled state from n copies of a mixed state σ_ABC⋅⋅⋅, there must be at least a subspace in the whole Hilbert space of all the copies such that the projection of σ_ABC⋅⋅⋅^⊗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.