Maximally incompatible quantum observables

By Teiko Heinosaari (Turku University)
Abstract: I will discuss a way to quantify the degrees of incompatibility of two observables in a probabilistic physical theory and, based on this, a global measure of the degree of incompatibility inherent in such theories, across all observable pairs. This makes it possible to compare probabilistic theories with respect to the nonclassical feature of incompatibility, raising many interesting questions. I will show that quantum theory contains observables that are as incompatible as any probabilistic physical theory can have. In particular, two of the most common pairs of complementary observables (position and momentum; number and phase) are maximally incompatible.