Moments of nonclassicality quasiprobabilities

A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments. Their relation to normally ordered moments is derived, which enables us to verify nonclassicality by using well established criteria. Alternatively, nonclassicality criteria are directly formulated in terms of nonclassicality moments. The latter converge in proper limits to the usually used criteria, as is illustrated for squeezing and sub-Poissonian photon statistics. Our theory also yields expectation values of any observable in terms of nonclassicality moments.

Figure 1

Dependence of the $Q_{\Omega }$ parameter on the filter width.

Figure 2

The blue area shows filter widths $w$ which uncover a negative $Q$ parameter for different mean thermal photon numbers.

Figure 3

The blue area shows filter widths $w$ which uncover the squeezing of the filtered quadrature variance ${\langle \Delta x^2\rangle }_{\tilde{\rho }}$, in dependence of the standard quadrature variance ${\langle \Delta x^2\rangle }_{\rho }$.