New Kochen-Specker Sets in Four Dimensions

Abstract

We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (of yes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component values from \{-1,0,1\} can be obtained by stripping vectors off a single system provided by Peres 20 years ago. In addition to them, we have found a number of other KS sets with 22 through 24 vectors. We present the algorithms we used and features we found, such as, for instance, that Peres' 24-24 KS set has altogether six critical KS subsets.

17 pages, 3 figures, 1 table; doi:10.1016/j.physleta.2010.03.019

References in corpus (8)

• Experimentally testable state-independent quantum contextuality
• 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
• Proposed experiment for testing quantum contextuality with neutrons
• Bipartite all-versus-nothing proofs of Bell's theorem with single-qubit measurements
• Quantum Computers, Discrete Space, and Entanglement

Cited by in corpus (24)

• 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
• Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
• 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
• Graph Approach to Quantum Systems
• Probabilistic Generation of Quantum Contextual Sets
• Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
• 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
• Parity proofs of the Kochen-Specker theorem based on the 120-cell
• New Class of 4-Dim Kochen-Specker Sets
• Automated generation of Kochen-Specker sets
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Hypergraph Contextuality
• On the connection between the theorems of Gleason and of Kochen and Specker
• Vector Generation of Contextual Sets
• Non-Kochen-Specker Contextuality
• Converting nonlocality into contextuality
• Nonclassical Structures within the N-qubit Pauli Group
• Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
• Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction