Gleason, Kochen-Specker, and a competition that never was

2012/01/01 by Ingemar Bengtsson · 6 citations
Computer Science · Mathematics · Medicine · Physics and Astronomy · #Algebra over a field #Calculus (dental) #Computer science #Discrete mathematics #Forcing (mathematics) #Hilbert space #Mathematical analysis #Mathematical economics #Mathematical proof #Mathematics #Medicine #Pure mathematics #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Space (punctuation) #quant-ph

paper · pdf · doi:10.1063/1.4773124

published in AIP conference proceedings, 125-135 (American Institute of Physics) · 8 pages, 2 figures; talk at the Vaxjo conference QTRF-6, 2012

openalex publication_date 2012/01/01 · arxiv created 2012/10/01 · arxiv updated 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

I review the two theorems referred to in the title, and then suggest that it would be interesting to know how much of Hilbert space one can use without forcing the proof of these theorems. It would also be interesting to know what parts of Hilbert space that are essential for the proofs. I go on to discuss cubes, graphs, and pentagrams.

Citations

• Twelve-dimensional Pauli group contextuality
• QBism, the Perimeter of Quantum Bayesianism
• (Non-)Contextuality of Physical Theories as an Axiom
• On the Problem of Hidden Variables in Quantum Mechanics
• Hidden Variables and the Two Theorems of John Bell
• IMPOSSIBLE OBJECTS: A SPECIAL TYPE OF VISUAL ILLUSION
• Quantum Theory: Concepts and Methods
• The Problem of Hidden Variables in Quantum Mechanics
• Measures on the Closed Subspaces of a Hilbert Space