I've read the following question: Negative probabilities in quantum physics and I'm not sure I understand all the details about my actual question. I think mine is more direct.
It is known that the Wigner function can become negative in certain region of phase-space. Some people claim that the negativity of this quasi-probability distribution signifies that the system behaves quantum mechanically (as opposed to classical physics, when probabilities are always positive). Apparently, there are still some controversies about this point. Please read the answers from the previously cited post: Negative probabilities in quantum physics
I would like to know whether there is an equivalence between the negativity of the Wigner distribution and some quantum behaviours or not. Is it still a question under debate / actual research or not ?
My main concern is that there are more and more experimental studies of the Wigner function (or other tomography captures) reporting negativity of the Wigner function. I would like to understand what did these studies actually probe.
As an extra question (that I could eventually switch to an other question): What is the quantum behaviour the negativity of the Wigner function may probe ?
Having not a lot of time at the moment, I would prefer an explicit answer rather than a bunch of (perhaps contradictory) papers regarding this subject. But I would satisfy myself with what you want to share of course :-)