Using a resource theoretic perspective to witness and engineer quantum generalized contextuality for prepare-and-measure scenarios

We use the resource theory framework of generalized contextuality as a tool for analyzing the structure of prepare-and-measure scenarios. We argue that this framework is capable of simplifying proofs for witnessing quantum contextuality and straightens known arguments regarding the robustness of experimental implementations thereof. As a case study, we witness quantum contextuality associated with any nontrivial noncontextuality inequality for a class of scenarios by noticing a connection between the resource theory and measurement simulability. We also expose a rule for composing behaviours that allows one to build complex scenarios from simpler ones, which provides an explanation of the non-contextual polytope structure for complex scenarios and facilitates finding possible quantum violations. In particular, we show that the state-dependent cloning scenario inherits contextuality from a simpler scenario, and we engineer a complex prepare-and-measure scenario that has quantum contextual violations for any noncontextuality inequality. Witnessing contextuality from the abstract formalism of resource theories represents a potential new framework for demonstrating quantum-over-classical advantages for practical tasks.