  In this paper we attempt to establish a theory of negative (quasi)
probability distributions from fundamental principles and apply it to the study
of the double-slit experiment in quantum mechanics. We do so in a way that
preserves the main conceptual issues intact but allow for a clearer analysis,
by representing the double-slit experiment in terms of the Mach-Zehnder
interferometer, and show that the main features of quantum systems relevant to
the double-slit are present also in the Mach-Zehnder. This converts the problem
from a continuous to a discrete random variable representation. We then show
that, for the Mach-Zehnder interferometer, negative probabilities do not exist
that are consistent with interference and which-path information, contrary to
what Feynman believed. However, consistent with Scully et al.'s experiment, if
we reduce the amount of experimental information about the system and rely on
counterfactual reasoning, a joint negative probability distribution can be
constructed for the Mach-Zehnder experiment.
