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

Abstract

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 strengthens known arguments regarding 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 behaviors 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 of Ref.[2] 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.

The rank of contextuality

“…Just to mention a few there is among them the zero-error channel capacity [11], quantum device-independent cryptography [12], magic-state based quantum computation [13,14], quantum computation using shallow circuits [15] and one-way communication [16], and capacity of multiple access channels [17]. For further development based on these seminal results, we refer the reader to [18,19] and the review [5].…”

The rank of contextuality

“…Just to mention a few there is among them the zero-error channel capacity [11], quantum device-independent cryptography [12], magicstate based quantum computation [13,14], quantum computation using shallow circuits [15] and one-way communication [16], and capacity of multiple access channels [17]. For further development based on these seminal results, we refer the reader to [18,19] and the review [5].…”