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 conceivable physical theories. Thus, GPT describing given theory necessarily includes all physically possible processes. We here consider question how provide GPT-like characterization particular experimental setup within theory. show that resulting is not generally in and itself, rather, it described by more general mathematical object we introduce term an accessible fragment. then equivalence relation, termed cone equivalence, between fragments (and, special case, standard GPTs). give number examples scenarios are best using fragments, where moreover, cone-equivalence arises naturally. prove fragment admits classical explanation if only every other equivalent also explanation. Finally, leverage this result several fundamental results regarding requirements for witnessing failure noncontextuality. In particular, neither incompatibility among measurements nor assumption freedom choice necessary failures noncontextuality, such can be witnessed even when arbitrarily inefficient detectors.