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

We develop three-mode generalizations of the Einstein-Podolsky-Rosen paradox, allowing us to define inequalities which may be used to indicate continuous-variable tripartite entanglement. We use these inequalities and an appropriate version of the previously developed van Loock-Furusawa inequalities to theoretically compare the continuous-variable tripartite entanglement available from the use of three concurrent x ⁽²⁾ nonlinearities and from three independent squeezed states mixed on beamsplitters. The text was submitted by the authors in English.