Accessible fragments of generalized probabilistic theories, cone equivalence, and applications to witnessing nonclassicality

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particular experimental setup within a given physical theory. We show that the resulting characterization is not generally a GPT in and of itself, rather, it is described by a more general mathematical object that we introduce and term an accessible GPT fragment. We then introduce an equivalence relation, termed cone equivalence, between accessible GPT fragments (and, as a special case, between standard GPTs). We give a number of examples of experimental scenarios that are best described using accessible GPT fragments, and where moreover, cone-equivalence arises naturally. We then prove that an accessible GPT fragment admits of a classical explanation if and only if every other fragment that is cone equivalent to it also admits of a classical explanation. Finally, we leverage this result to prove several fundamental results regarding the experimental requirements for witnessing the failure of generalized noncontextuality. In particular, we prove 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.

Automated summary

The formalism of generalized probabilistic theories (GPTs) was developed to characterize conceivable physical theories. The GPT describing a specific physical theory includes all possible processes. This study introduces an accessible GPT fragment to describe the characteristics of a particular experimental setup within a physical theory. Cone equivalence is defined as an equivalence relation between accessible GPT fragments. Several examples are given to demonstrate the use of accessible GPT fragments in experimental scenarios, and it is proven that failures of generalized noncontextuality can be witnessed without incompatibility among measurements or the assumption of freedom of choice.