  A large number of inequalities have been proposed for the detection of
bipartite continuous variable entanglement and Einstein-Podolsky-Rosen
steering. Many of these are based on either measured or inferred variances and
are relatively easily measured via homodyne detection of optical outputs. In
this work we examine a number of bipartite inequalities in the process of
cascaded downconversion and sum-frequency generation inside an optical cavity.
This has previously been predicted to be a potential source of
continuous-variable tripartite entanglement, therefore we know that there are
no separable bipartitions. In this work we investigate the performance of the
chosen inequalities in the stable, below threshold regime. We show that
detection of the existing entanglement is sensitive to the actual inequalities
chosen, with some criteria missing it completely. Our results are explained by
the fact that violation of the chosen inequalities is sufficient but not
necessary to demonstrate the non-classical relationships between the modes, and
highlights the outstanding problem of developing a reliable continuous-variable
entanglement measure.
