I can't seem to find a definition for genuine entanglement but it is being used in an article I'm reading and the references inside but I'm unable to find the precise definition.
One thing I was able to get to the bottom of is "So far, genuine multipartite entangled (GME) states in the form of Greenberger-HorneZeilinger (GHZ) states..", but I do not know what about the GHZ states makes them "genuinely entangled".
Also the way it comes up is "genuine multipartite entanglement", which begs the questions (after what is genuine entanglement) why does it only come up in multipartite schemes ($n>2$)?