The University of Hong Kong, Hong Kong, ravi@cs.hku.hk
(joint work with Yuan Liu, Karol Horodecki, Monika Rosicka and Paweł Horodecki)
Applications of the foundational Kochen-Specker (KS) theorem have attracted much interest recently. Here, we show that measurement structures within KS proofs termed gadgets provide an optimal toolbox for contextuality applications including (i) constructing classical channels exhibiting entanglement-assisted advantage in zero-error communication, (ii) finding optimal tests for contextuality-based semi-device-independent randomness generation, and (iii) identifying large separations between quantum theory and binary generalised probabilistic theories. Finally, we introduce a higher-order generalisation of gadgets that we show exist within general KS proofs, and use them to construct novel proofs of the KS theorem.
[1] Y. Liu, R. Ramanathan, K. Horodecki, M. Rosicka, P. Horodecki. Optimal Measurement Structures for Contextuality Applications. arXiv:2206.13139 (2022).