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. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of classicality is the existence of a generalized-noncontextual ontological model. In particular, this notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We leverage this fact to demonstrate that measurement incompatibility is neither necessary nor sufficient for proofs of the failure of generalized noncontextuality. Furthermore, we show that every proof of the failure of generalized noncontextuality in a quantum prepare-measure scenario can be converted into a proof of the failure of generalized noncontextuality in a corresponding scenario with no incompatible measurements.

Automated summary

Incompatible measurements are often seen as a characteristic of quantum theory that distinguishes it from classical worldviews. However, a more general notion of classicality is the existence of a generalized-noncontextual ontological model. This notion can imply constraints on the representation of outcomes even within a single nonprojective measurement. We demonstrate that measurement incompatibility is not necessary nor sufficient for proofs of the failure of generalized noncontextuality, and that every proof of the failure of generalized noncontextuality can be converted into a corresponding scenario without incompatible measurements.