Multi-particle entanglement via two-party entanglement

Entanglement between n particles is a generalization of the entanglement be tween two particles, and a state is considered entangled if it cannot be wr itten as a mixture of tensor products of the n particles' states. We presen t the key notion of semi-separability, used to investigate n-particle entan glement by looking at two-party entanglement between its various subsystems . We provide necessary conditions for n-particle separability (that is, suf ficient conditions for n-particle entanglement). We also provide necessary and sufficient conditions in the case of pure states. By surprising example s, we show that such conditions are not sufficient for separability in the case of mixed states, suggesting entanglement of a strange type.