Adam Mickiewicz University in Poznan, Poland, pawel.kurzynski@amu.edu.pl
(joint work with Kelvin Onggadinata and Dagomir Kaszlikowski)
It is not possible to construct a joint probability distribution (JPD) for any set of Kochen-Specker (KS) measurements, simply because the KS theorem states that there is no joint set of outcomes over which such distribution can be constructed. However, we show it is possible to construct a joint quasi-probability distribution (JQD) over any KS set. The idea is to relax the completeness assumption. Interestingly, the completeness emerges at the level of measurable marginal probability distributions, therefore our construction is consistent with any observable data. The emergence of completeness occurs due to the negativity of the JQD. Our approach allows to treat state-independent and state-dependent contextuality on equal footing and to use the negativity as a measure of nonclassicality in both scenarios.
[1] K. Onggadinata, D. Kaszlikowski, and P. Kurzynski, arXiv:2210.06822 (2022)