Gadget structures in proofs of the Kochen-Specker theorem
1Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
2Institute of Theoretical Physics and Astrophysics and the National Quantum Information Centre, Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-308 Gdansk, Poland.
3Institute of Informatics Faculty of Mathematics, Physics and Informatics, University of Gdansk, 80-308 Gdansk, Poland
4International Centre for Theory of Quantum Technologies, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland
5Laboratoire d'Information Quantique, Université Libre de Bruxelles, Belgium
6International Centre for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland
7Faculty of Applied Physics and Mathematics, National Quantum Information Centre, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
|Published:||2020-08-14, volume 4, page 308|
|Citation:||Quantum 4, 308 (2020).|
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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 .
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