Sampling of quasidistributions, nonclassical behavior and negative probabilities

• Joint quasidistributions for parametric down conversion in nonclassical region are derived.
• These quasidistributions are sampled with the use of the Shannon–Kotelnikov theorem.
• The sampling is used for interpretation of negative probabilities in nonclassical region.

We perform a sampling of the quasidistribution for the process of optical down-conversion in nonclassical regime, in which negative values of the quasidistribution are exhibited, using the Shannon–Kotelnikov sampling formula. We show that negative values of the quasidistribution do not directly represent probabilities, however, negative terms in the sampling formula related to the nonclassical behavior can be interpreted as positive probabilities in the negative orthogonal sinc-basis, whereas positive probabilities in the positive sinc-basis describe classical cases.