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

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