Modeling Generalized Squeezed States

We consider the general problem of modeling an n-photon entangled state by a squeezed vacuum state using a squeezing operator given by a squeezing tensor of rank n. We derived a simple recursion relation for generating the Bogoliubov transformed creation and annihilation operators and use this result to express the generalized squeezed state as an equivalent complex Gaussian random vector. Finally, we compare low-order approximations of the squeezed state to entangled multi-photon Greenberger-Horne-Zeilinger (GHZ) states using post-selection and a deterministic detector model. We find that this classical model is capable of exhibiting violations of the Mermin inequality consistent with experimental observations.