Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen correlations from triple nonlinearities

We compare theoretically the tripartite entanglement available from the use of three concurrent $\chi^{(2)}$ nonlinearities and three independent squeezed states mixed on beamsplitters, using the van Loock-Furusawa inequalities. We also define three-mode generalisations of the Einstein-Podolsky-Rosen paradox which are an alternative for demonstrating the inseparability of the density matrix.