Gadget structures in proofs of the kochen-specker theorem

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Abstract

The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term 01-gadgets, that capture the essential contradiction necessary to prove the Kochen-Specker theorem, i.e,. every Kochen-Specker graph contains a 01-gadget and from every 01-gadget one can construct a proof of the Kochen-Specker theorem. Moreover, we show that the 01-gadgets form a fundamental primitive that can be used to formulate state-independent and state-dependent statistical Kochen-Specker arguments as well as to give simple constructive proofs of an “extended” Kochen-Specker theorem first considered by Pitowsky in [22].

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Ramanathan, R., Rosicka, M., Horodecki, K., Pironio, S., Horodecki, M., & Horodecki, P. (2020). Gadget structures in proofs of the kochen-specker theorem. Quantum, 4. https://doi.org/10.22331/Q-2020-08-14-308

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