Criteria for genuine N -partite continuous-variable entanglement and Einstein-Podolsky-Rosen steering
Run Yan Teh, M. D. Reid · Physical Review A · 2014
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.