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arXiv:1509.03618 · Journal of Algebra

A Kochen–Specker theorem for integer matrices and noncommutative spectrum functors

Michael Ben-Zvi, Alexander Ma, Manuel L. Reyes, Alexandru Chirvasitu

Published Aug 22, 2017• 4 citations
arXivHTMLPDF
DOI
10.1016/j.jalgebra.2017.08.008

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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 \cite{Pitowsky}.