Generation and distillation of non-Gaussian entanglement from nonclassical photon statistics

Abstract

With a product state of the form ρ_in = ρ_a⊗ |0 ›_bb ‹ 0| as input to a beam splitter, the output two-mode state ρ out is shown to be negative under partial transpose (NPT) whenever the photon number distribution (PND) statistics { ρ (n a ) } associated with the possibly mixed state ρ a of the input a-mode is antibunched or otherwise nonclassical, i.e., whenever { ρ (n a ) } fails to respect any one of an infinite sequence of necessary and sufficient classicality conditions. Negativity under partial transpose turns out to be a necessary and sufficient test for entanglement of ρ out which is generically non-Gaussian. The output of a PND distribution is further shown to be distillable if any one of an infinite sequence of three term classicality conditions is violated.