System loophole of generalized noncontextuality

Generalized noncontextuality is a well-studied notion of classicality that is applicable to a single system, as opposed to Bell locality. It relies on representing operationally indistinguishable procedures identically in an ontological model. However, operational indistinguishability depends on the set of operations that one may use to distinguish two procedures: we refer to this set as the reference of indistinguishability. Thus, whether or not a given experiment is noncontextual depends on the choice of reference. The choices of references appearing in the literature are seldom discussed, but typically relate to an implicit notion of a system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment This question depends in part on one's beliefs in the universe being fundamentally continuous or fundamentally composite. To draw a coherent picture of the possible approaches one may use, we start by formulating a notion of noncontextuality for prepare-and-measure scenarios with respect to an explicit reference of indistinguishability. We investigate how verdicts of noncontextuality depend on this choice of reference, and in the process we introduce the concept of the noncontextuality graph of a prepare-and-measure scenario. We then discuss several proposals that one may appeal to in order to fix the reference to a specific choice, and we relate these proposals to different conceptions of what a system really is. With this discussion, we advocate that whether or not an experiment is noncontextual is not as absolute as often perceived.