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

With a product state of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rho}_{\rm in} = {\rho}_{a} \otimes |0 \rangle_b {_b} \langle 0|}$$\end{document} as input to a beam splitter, the output two-mode state ρout is shown to be negative under partial transpose (NPT) whenever the photon number distribution (PND) statistics { p(na) } associated with the possibly mixed state ρa of the input a-mode is antibunched or otherwise nonclassical, i.e., whenever { p(na) } 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 ρout 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.