Contextuality without Incompatibility

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview.

However, I will demonstrate that measurement incompatibility is neither necessary nor sufficient for nonclassicality relative to one of our best notions of classical explainability, namely the existence of a generalized noncontextual ontological model. Furthermore, I will show that every proof of the failure of generalized noncontextuality in a prepare-measure scenario can be converted into a second proof in a corresponding scenario which has no incompatible measurements. This is then shown to imply that neither incompatibility among measurements nor the assumption of freedom of choice is necessary for witnessing failures of generalized noncontextuality, and moreover, that such failures can be witnessed even when using arbitrarily inefficient detectors. Along the way, I will introduce several new ideas that are useful for the study of generalized probabilistic theories.