MARGINAL DISTRIBUTIONS OF QUASI-PROBABILITIES IN QUANTUM OPTICS

Marginal properties of arbitrary s-ordered quasiprobability distributi on functions are investigated. The positivity of marginal distribution s for an quasiprobabilities, interpolating between the Wigner function and the Q representation of the density operator (s less-than-or-equa l-to 0), is proven. We also show that, on the contrary, marginal distr ibutions of the remaining quasiprobabilities, interpolating between th e Wigner function and the P representation (s > 0), can take on negati ve values. General formulas for the marginal distributions are given, and their relations to the actual quantum-mechanical probability distr ibutions for position and momentum are established. Our results provid e an interesting generalization of some recent results concerning marg inal properties of the P representation [G.S. Agarwal, Opt. Commun. 95 , 109 (1993)].