On the connection between the theorems of Gleason and of Kochen and Specker

Abstract

We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of a function $m$ on the unit sphere. In the case of Gleason's theorem the entire unit sphere needs to be considered, while a finite set of points suffices to prove the Kochen-Specker theorem.

8 pages, 5 figures

References in corpus (6)

• Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements
• Value-indefinite observables are almost everywhere
• Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
• Generalized Complex Spherical Harmonics, Frame Functions, and Gleason Theorem
• Gleason, Kochen-Specker, and a competition that never was
• Quantum Collapse Bell Inequalities

Cited by in corpus (2)

• Quantum Contextuality
• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality