Kochen—Specker Theorem

Cecilia Flori

Guillermo Morales Luna

Andrew Lenard

Jose Luis Cereceda

Ravishankar Ramanathan, Monika Rosicka, Karol Horodecki +3 more

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}.

Ahmed Barbar

This essay provides an analysis of two important theorems that arise in the context of quantum mechanics: the Kochen-Specker theorem, which challenges the existence of hidden variable theories; and the Conway-Kochen (free will) theorem, which can be seen as an improvement over the Kochen-Specker theorem, but instead focuses on challenging determinism.