High Quality Content by WIKIPEDIA articles! A quasiprobability distribution is a mathematical object similar to a probability distribution but relaxing some of the 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.