Contextuality as a Noise-robust Witness of Nonclassicality: Beyond the Cabello-Severini-Winter Framework*

We propose an approach to obtaining noise-robust noncontextuality inequalities within the framework of generalized noncontextuality, inspired by statistical proofs of the Kochen-Specker (KS) theorem. This approach works for any such proof of the KS theorem and violation of the resultant noncontextuality inequalities can witness contextuality even if the measurements or preparations in the experiment are noisy or unsharp. Indeed, this approach allows us to generalize the graph-theoretic Cabello-Severini-Winter (CSW) framework to a noise-robust hypergraph-theoretic framework. For the case of quantum theory, we can deal with nonprojective (or unsharp) measurements and resolve the pathologies they lead to in traditional approaches such as CSW. Our noncontextuality inequalities are thus robust to the presence of noise in the experimental procedures, whether they are measurements or preparations, and are applicable to operational theories that need not be quantum.