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

With a product state of the form rho(in) = rho(a) circle times vertical bar 0 >(bb)< 0 vertical bar as input to a beam splitter, the output two-mode state rho(out) is shown to be negative under partial transpose (NPT) whenever the photon number distribution (PND) statistics {p(n(a))} associated with the possibly mixed state rho(a) of the input a-mode is antibunched or otherwise nonclassical, i.e., whenever {p(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 rho(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.