  We examine the tripartite entanglement properties of an optical system using
interlinked $\chi^{(2)}$ interactions, recently studied experimentally in terms
of its phase-matching properties by Bondani et al [M. Bondani, A. Allevi, E.
Gevinti, A. Agliati, and A. Andreoni, arXiv:quant-ph/0604002.]. We show that
the system does produce output modes which are genuinely tripartite entangled
and that detection of this entanglement depends crucially on the correlation
functions which are measured, with a three-mode Einstein-Podolsky-Rosen
inequality being the most sensitive.
