Classification of multipartite systems featuring only and genuine entangled states

Abstract

We present several multipartite quantum systems featuring the same type of genuine (tripartite) entanglement. Based on a geometric interpretation of the so-called and states we show that the classification of all multipartite systems featuring those and only those two classes of genuine entanglement can be deduced from earlier work of algebraic geometers. In this paper, non-entangled pure states are identified with the highest weight orbit of the SLOCC group acting on the corresponding Hilbert space.