  We introduce the pinching operator, which extends the theory of squeezing
operators to cubic and higher order non-Gaussian operators, and use it to
approximate $n$-photon entangled states using a pinched vacuum state and
pinching tensor of rank $n$. A simple recursion relation is derived for
generating the Bogoliubov transformed creation and annihilation operators,
which may be used to express the pinched state as a statistically equivalent
set of nonlinearly transformed complex Gaussian random variables. Using this
representation, we compare low-order approximations of the pinched state to
entangled multiphoton Fock states, such as Greenberger-Horne-Zeilinger (GHZ)
and W states. Using post-selection and a threshold detector model to represent
non-Gaussian measurements, we find that this model is capable of producing
states with a fidelity comparable to that of experimentally prepared
multiphoton entangled states. In particular, we obtain a Mermin statistic of
$5.27 \pm 0.01$ for a five-photon GHZ state, violating the noncontexuality
threshold by 127 standard deviations.
