Pinching operators for approximating multiphoton entangled states

We introduce the pinching operator, which extends the theory of squeezing operators to 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. Our results show that it is possible to classically simulate large multiphoton entangled states to high fidelity within the constraints of finite detection efficiency.