Recursive proof of the Bell-Kochen-Specker theorem in any dimension
arXiv:quant-ph/0504217 · doi:10.1016/j.physleta.2005.03.067
Abstract
We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension from a similar set in dimension (). As an application of the method we find the smallest proofs known in dimension five (29 vectors), six (31) and seven (34), and different sets matching the current record (36) in dimension eight.
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- Universality of state-independent violation of correlation inequalities for noncontextual theories
- Kochen-Specker set with seven contexts
- Proofs of the Kochen-Specker theorem based on a system of three qubits
- Necessary and sufficient conditions for state-independent measurement contextual scenarios
- Proofs of the Kochen-Specker theorem based on the N-qubit Pauli group
- Quantum Contextuality
- Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
- Quantum social networks
- Certifying sets of quantum observables with any full-rank state
- State-independent contextuality with identical particles
- Automated generation of Kochen-Specker sets
- The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
- The Collapse of Bell Determinism
- Automated Generation of Arbitrarily Many Kochen-Specker and Other Contextual Sets in Odd Dimensional Hilbert Spaces
- Kochen-Specker Sets with a Mixture of 16 Rank-1 and 14 Rank-2 Projectors for a Three-Qubit System
- Construction of State-independent Proofs for Quantum Contextuality
- Optimal conversion of Kochen-Specker sets into bipartite perfect quantum strategies
- Two fundamental solutions to the rigid Kochen-Specker set problem and the solution to the minimal Kochen-Specker set problem under one assumption
- Non-bicolourable Finite Configurations of Rays and Their Deformations
- Supersinglets can be self-tested with perfect quantum strategies
- Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
- Generation of Kochen-Specker contextual sets in higher dimensions by dimensional upscaling whose complexity does not scale with dimension and their applications