The York Research Database

We introduce a new way of quantifying the degrees of incompatibility of two observables in a probabilistic physical theory and, based in this, a global measure of the incompatibility of such theories. This open up an novel and flexible way of comparing probabilistic theories with respect to the nonclassical feature of incompatibility, raising many interesting questions, some of which will be answered here. We show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have if arbitrary pairs of observables are considered. If one adopts a more refined measure of incompatibility, for instance, by restricting the comparison to binary observables, it turns out that there are probabilistic theories that are more incompatible than quantum mechanics.