  We examine the implications of several recently derived conditions [Hillery
and Zubairy, Phys. Rev. Lett. 96, 050503 (2006)] for determining when a
two-mode state is entangled. We first find examples of non-Gaussian states that
satisfy these conditions. We then apply the entanglement conditions to the
study of several linear devices, the beam splitter, the parametric amplifier,
and the linear phase-insensitive amplifier. For the first two, we find
conditions on the input states that guarantee that the output states are
entangled. For the linear amplifier, we determine in the limit of high and no
gain, when an entangled input leads to an entangled output. Finally, we show
how application of two two-mode entanglement conditions to a three-mode state
can serve as a test of genuine three-mode entanglement.
