Gaussian versus Non-Gaussian Filtering of Phase-Insensitive Nonclassicality

Measures of quantum properties are essential to understanding the fundamental differences between and classical systems as well quantifying resources for technologies. Here two broad classes bosonic phase-space functions, which filtered versions Glauber-Sudarshan $P$ function, compared with regard their ability uncover nonclassical effects light through negativities. Gaussian filtering function yields family $s$-parametrized quasiprobabilities, while more powerful regularized nonclassicality quasiprobabilities obtained by non-Gaussian filtering. A method is proposed directly sample such functions restricted case phase-independent states from balanced homodyne measurements. This overcomes difficulties previous approaches that manually append uniformly distributed optical phases measured quadrature data. We experimentally demonstrate this technique heralded single- two-photon using detection varying efficiency. The can be sampled, non-negative efficiencies below 0.5. By contrast, we show significant negativities even low efficiencies.