Direct sampling of a smoothed Wigner function from quadrature distributions

Abstract

We propose the reconstruction of a smoothed Wigner function from quadrature distributions instead of the Wigner function itself to avoid the problems with the inverse Radon transformation. Starting from the well known relation between s-parametrized quasiprobability distributions W(x,p,s) and quadrature component distributions w(x,), we show that the sampling function needed to determine a smoothed Wigner function W(x,p,-|s|) is basically a shifted and scaled version of the well known pattern function necessary to reconstruct the probability of finding no photon in the signal field. An analogous result has been recently found in the literature. Here we obtain this result in a very concise and alternative way.