Gadget Structures in Proofs of the Kochen-Specker Theorem

Abstract

The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show (in [1]) that within every Kochen-Specker graph, there exist interesting subgraphs which we term 01-gadgets [2], 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 [3]. We conclude with some recent developments on the topic. [1] R. Ramanathan, M. Rosicka, K. Horodecki, S. Pironio, M. Horodecki and P. Horodecki. Gadget structures in proofs of the Kochen-Specker theorem. arXiv: 1807.00113 (2018). [2] R. K. Clifton. Getting Contextual and Nonlocal Elements of Reality the Easy Way. American Journal of Physics, 61: 443 (1993). [3] I. Pitowsky. Infinite and finite Gleason’s theorems and the logic of indeterminacy. Journal of Mathematical Physics 39, 218 (1998).