A quasiprobability distribution is a mathematical object similar
to a probability distribution but which relaxes some of
Kolmogorov's axioms of probability theory. Although
quasiprobabilities share many of the same general features of
ordinary probabilities such as the ability to take expectation
values with respect to the weights of the distribution, they all
violate the third probability axiom because regions integrated
under them do not represent probabilities of mutually exclusive
states. To compensate, some quasiprobability distributions also
counterintuitively have regions of negative probability density,
contradicting the first axiom. Quasiprobability distributions
arise naturally in the study of quantum mechanics when treated
in the phase space formulation, commonly used in quantum optics,
time-frequency analysis, and elsewhere. In the most general
form, the dynamics of a quantum-mechanical system are determined
by a master equation in Hilbert space: an equation of motion for
the density operator (usu