Criteria for genuine N -partite continuous-variable entanglement and Einstein-Podolsky-Rosen steering

Following previous work, we distinguish between genuine N-partite entanglement and full N-partite inseparability. Accordingly, we derive criteria to detect genuine multipartite entanglement using continuous-variable (position and momentum) measurements. Our criteria are similar but different to those based on the van Loock-Furusawa inequalities, which detect full N-partite inseparability. We explain how the criteria can be used to detect the genuine N-partite entanglement of continuous variable states generated from squeezed and vacuum state inputs, including the continuous-variable Greenberger-Horne-Zeilinger state, with explicit predictions for up to N=9. This makes our work accessible to experiment. For N=3, we also present criteria for tripartite Einstein-Podolsky-Rosen (EPR) steering. These criteria provide a means to demonstrate a genuine three-party EPR paradox, in which any single party is steerable by the remaining two parties.