Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions

Abstract

It is pointed out that the 60 complex rays in four dimensions associated with a system of two qubits yield over 10^9 critical parity proofs of the Kochen-Specker theorem. The geometrical properties of the rays are described, an overview of the parity proofs contained in them is given, and examples of some of the proofs are exhibited.

17 pages, 13 tables, 3 figures. Several new references have been added

References in corpus (15)

• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• Specker's Parable of the Over-protective Seer: A Road to Contextuality, Nonlocality and Complementarity (PLUS AN ERRATUM)
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• Three criteria for quantum random number generators based on beam splitters
• Projective Ring Line Encompassing Two-Qubits
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Cited by in corpus (23)

• 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
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Quantum Contextuality
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• What makes quantum clicks special?
• Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces
• Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
• Contextuality with a Small Number of Observables
• Parity proofs of the Kochen-Specker theorem based on the 120-cell
• GHZ paradoxes based on an even number of qubits
• The Penrose dodecahedron and the Witting polytope are identical in CP(3)
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Automated generation of Kochen-Specker sets
• Primitive Nonclassical Structures of the $N$-qubit Pauli Group
• Hypergraph Contextuality
• Vector Generation of Contextual Sets
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction
• Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
• Construction of Three-Qubit Kochen-Specker Sets