Engineering and Applying Quantum Contextuality

The endeavor to refute hidden variable theories underlying quantum theory has yielded the discipline of contextual sets. A plethora of various kinds of sets of arbitrary structure in any dimension have been developed, alongside extensive experimental validation. These advancements incited us to investigate to what extent we might move beyond hidden variables, engineer contextual sets, and find their applications within quantum theory itself, without any reference to hidden variable models. To this end, we consider possible applications of contextual sets in quantum computation, cryptography, pseudo-telepathy, and nonlocality, as well as generating them from error-correction protocols, complex Hadamard gates, and simple quantum gates. We found that the results in this field are still scarce, and we therefore investigated the directions in which future research might be carried out and the potential obstacles to realizing such undertakings in the past.