  Purification schemes for multi-particle entangled states cannot be treated as
straightforward extensions of those for two particles because of the lack of
symmetry they possess. We propose purification protocols for a wide range of
mixed entangled states of many particles. These are useful for understanding
entanglement, and will be of practical significance in multi-user cryptographic
schemes or distributed quantum computation and communication. We show that
operating locally on multi-particle entangled states directly is more efficient
than relying on two-particle purification.
