Non-locality and "quantum non-contextuality"
Quantum theory permits non-local correlations. The violation of Bell's inequalities is equivalent with proving the non-existence of a joint probability distribution defined on the space of counterfactual outcomes that return the experimental probabilities as marginals. On the other hand, the existence of such joint probability distribution would signify (classical) non-contextuality.
Inspired by path integral formulations of quantum theory, we define a quantum analogue of the joint probability distribution which we term "quantum non-contextuality". We require the existence of a joint strongly-positive quantum measure, which is the most natural generalisation of probability measure from a "histories" perspective. This condition, while it includes all the correlations allowed by quantum theory, it restricts the non-local correlations giving (up to some nuances) the "almost quantum correlations" of Navascues et al (2014). This set of correlations appears as a good candiate for generalisations of quantum theory.
- Dowker, Henson, Wallden, New J. Phys. 16 (2014) 033033