What is quasi-probability distribution? Why is it important in quantum mechanics? What does "quasi" mean?

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    $\begingroup$ You might find this finance application helpful. Essentially, at least one of the 3 Kolmogorov axioms of probability is violated. In this case, a negative probability might be used to give a value to something. It seems that the price of the financial asset would be 0.5 but theoretically it can't be determined under probability distributions. Hence, there are quasiprobability distributions $\endgroup$
    – BCLC
    Commented Dec 15, 2015 at 23:27

1 Answer 1


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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    $\begingroup$ ckrk, quasiprobability distributions relax at least one of the Kolmogorov axioms not necessarily nonnegativity of probability, I think: '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' $\endgroup$
    – BCLC
    Commented Dec 15, 2015 at 23:28
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    $\begingroup$ @BCLC according to wikipedia you are right, i was under the opinion that quasi probabilities specificly refet to distributions that include negative weights! Possibly i was confused by the naming convention of norms, where quasi- and pseudo- refer to relaxation to different specific axioms. Ill edit accordingly. $\endgroup$
    – ckrk
    Commented Dec 17, 2015 at 19:30

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