Kochen-Specker contextuality

A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here compatible measurements are those that can be implemented simultaneously or, more generally, those that are jointly measurable. This conflict is generically called quantum contextuality. In this review, an introduction to this subject and its current status is presented. Several proofs of the Kochen-Specker theorem and different notions of contextuality are reviewed. How to experimentally test some of these notions is explained, and connections between contextuality and nonlocality or graph theory are discussed. Finally, some applications of contextuality in quantum information processing are reviewed.

Automated summary

This article introduces the Kochen-Specker theorem, a central result in the foundations of quantum mechanics, and its conflict with classical models. It reviews several proofs of the theorem and different notions of contextuality, and discusses the connections between contextuality and nonlocality or graph theory. Finally, it reviews the applications of contextuality in quantum information processing.