What is quasi-probability distribution? Why is it important in quantum mechanics? What does "quasi" mean?
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A quasi probability distribution relaxes an axiom of probabilty. In the context of Quantum Mechanics,it is specificly the axiom of probability that requires $p_{i} \geq 0$. So the sum of the distribution can include negative terms!
Quantum mechanics allows for events with a negative expectation values, to acount for phenomena like destructive interference. Intuitively The negative expectation values make it possible for events to "cancel out" another event with different sign. This would not be possible with non negative numbers. A distribution of these expectation values, that is normalized to one can be seen as a quasi probability.
Im sorry if this answer is a bit untechnical, but its all i could make up quickly and i hope for a quick read its enough . I think Scott Aaronson has an excellent and pedagogical in depth post, exactly telling you why quasi probabilites come up in QM, better than i could ever do. Refer to: http://www.scottaaronson.com/democritus/lec9.html
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