Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres

Abstract

A diagrammatic representation is given of the 24 rays of Peres that makes it easy to pick out all the 512 parity proofs of the Kochen-Specker theorem contained in them. The origin of this representation in the four-dimensional geometry of the rays is pointed out.

14 pages, 6 figures and 3 tables. Three references have been added. Minor typos have been corrected

References in corpus (11)

• Hidden Variables and the Two Theorems of John Bell
• A simple test for hidden variables in spin-1 system
• State-independent experimental test of quantum contextuality
• Experimental test of quantum contextuality in neutron interferometry
• State-independent quantum contextuality with single photons
• Testing contextuality on quantum ensembles with one clean qubit
• Universality of state-independent violation of correlation inequalities for noncontextual theories
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• Pentagrams and paradoxes
• New Kochen-Specker Sets in Four Dimensions
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Cited by in corpus (14)

• Kochen-Specker Contextuality
• Kochen-Specker set with seven contexts
• Proofs of the Kochen-Specker theorem based on a system of three qubits
• Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
• On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits
• Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
• Quantum Contextuality
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• Contextuality with a Small Number of Observables
• Contextuality degree of quadrics in multi-qubit symplectic polar spaces
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Primitive Nonclassical Structures of the $N$-qubit Pauli Group
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
• Construction of Three-Qubit Kochen-Specker Sets