Optimal measurement structures for contextuality applications

Abstract The Kochen-Specker (KS) theorem is a cornerstone result in the foundations of quantum mechanics describing fundamental difference between theory and classical non-contextual theories. Recently specific substructures termed 01-gadgets were shown to exist within KS proofs that capture essential contradiction theorem. Here, we show these gadgets their generalizations provide an optimal toolbox for contextuality applications including (i) constructing channels exhibiting entanglement-assisted advantage zero-error communication, (ii) identifying large separations binary generalized probabilistic theories, (iii) finding tests contextuality-based semi-device-independent randomness generation. Furthermore, introduce study generalization definite prediction sets more general logical propositions, term higher-order gadgets. We pinpoint role play by as induced subgraphs graphs showing how construct state-independent using building blocks. constructions developed here may help solving some remaining open problems regarding minimal