The Wigner Function as Distribution Function

GERALD J. IAFRATE, H. L. Grubin, David K. Ferry

M. Horibe, Akiyoshi Takami, T. Hashimoto +1 more

For the Wigner function of a system in N-dimensional Hilbert space, we propose the condition, which ensures that the Wigner function has correct marginal distributions along tilted lines. Under this condition we get the Wigner function without ambiguity if N is odd. If N is even, the Wigner function does not exist.

Ulf Leonhardt, Henryk Paul

Although the reconstruction of the Wigner function from generalized quasiprobability distributions that can be interpreted as smoothed Wigner functions poses no problem for theoretical calculations, there are, however, difficulties in the reconstruction when those distributions are gained from measurements.

Gen-ichi Hatakoshi

Joachim J. Włodarz

Th. Richter

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.