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arXiv · 1807.00113

Gadget structures in proofs of the Kochen-Specker theorem

Ravishankar Ramanathan·Monika Rosicka·Karol Horodecki·Stefano Pironio·Michał Horodecki·Paweł Horodecki
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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.

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Ravishankar Ramanathan, Monika Rosicka, Karol Horodecki, Stefano Pironio, Michał Horodecki, Paweł Horodecki. 2018-06-30. Gadget structures in proofs of the Kochen-Specker theorem. https://doi.org/10.22331/q-2020-08-14-308

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