Multipartite Entanglement

Summary

This chapter generalizes entanglement theory from two‐partite to multipartite systems and reviews the developments of this theory. It then considers multiparticle entanglement of pure quantum states. It is natural to ask whether there is entanglement measures that quantify the “degree of multipartite entanglement” found in a state. There are two approaches to defining entanglement measures: the axiomatic and the operational one. The chapter discusses these two approaches. Next, it describes important classes of multipartite quantum states that admit an efficient classical description ‐ including matrix product states, stabilizer states, and bosonic and fermionic Gaussian states ‐ and sketches their roles in quantum information theory. Then, it surveys a variety of very different and largely independent aspects of multipartite entanglement. The purpose of these examples is to give a feeling for the breadth of the field.