On the system loophole of generalized noncontextuality

TL;DR

This paper explores how the definition of noncontextuality in quantum systems depends on the chosen reference of indistinguishability, revealing a system loophole that challenges the notion's objectivity.

Contribution

It introduces the concept of relative noncontextuality, analyzes its dependence on reference choices, and discusses implications for defining the underlying system in quantum experiments.

Findings

Noncontextuality depends on the reference of indistinguishability.

Introduces the noncontextuality graph for prepare-and-measure scenarios.

Highlights the relativity of noncontextuality judgments based on reference choices.

Abstract

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 a notion of system underlying the experiment. This shift in perspective then begs the question: how should one define the extent of the system underlying an experiment? Our paper primarily aims at exposing this question rather than providing a definitive answer to it. We start by formulating a notion of relative noncontextuality for prepare-and-measure scenarios, which is simply noncontextuality with respect to an explicit reference of indistinguishability. We investigate how verdicts of relative noncontextuality depend on this choice of reference, and in the process 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 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.