Proofs of the Kochen-Specker theorem based on a system of three qubits

Abstract

A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based proofs leads to a system of projectors and bases that generally yields a large number of "parity proofs" of the Kochen-Specker theorem. Some examples of such proofs are given and some of their applications are discussed.

Some typos and minor errors have been corrected

References in corpus (14)

• Hidden Variables and the Two Theorems of John Bell
• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• Experimental test of quantum contextuality in neutron interferometry
• State-independent proof of Kochen-Specker theorem with 13 rays
• State-independent quantum contextuality with single photons
• Logical Bell Inequalities
• Universality of state-independent violation of correlation inequalities for noncontextual theories
• Greenberger-Horne-Zeilinger Nonlocality in Arbitrary Even Dimensions
• Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
• Entanglement Patterns in Mutually Unbiased Basis Sets for N Prime-state Particles
• Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
• Minimal Kochen-Specker theorem in finite dimensions

Cited by in corpus (36)

• Kochen-Specker Contextuality
• Quantifying Contextuality
• 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
• Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen-Specker theorem: the Peres-Mermin square
• Rotational covariance and GHZ contradictions for three or more particles of any dimension
• Confined Contextuality in Neutron Interferometry: Observing the Quantum Pigeonhole Effect
• Distinguished three-qubit 'magicity' via automorphisms of the split Cayley hexagon
• Parity proofs of the Kochen-Specker theorem based on the Lie algebra E8
• 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
• Mermin pentagrams arising from Veldkamp lines for three qubits
• The magic three-qubit Veldkamp line: A finite geometric underpinning for form theories of gravity and black hole entropy
• Practical and efficient experimental characterization of multiqubit stabilizer states
• Five-Qubit Contextuality, Noise-Like Distribution of Distances Between Maximal Bases and Finite Geometry
• GHZ paradoxes based on an even number of qubits
• Benchmarks of Nonclassicality for Qubit Arrays
• Primitive Nonclassical Structures of the $N$-qubit Pauli Group
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Automated generation of Kochen-Specker sets
• Hypergraph Contextuality
• Gleason, Kochen-Specker, and a competition that never was
• New Examples of Kochen-Specker Type Configurations on Three Qubits
• 'Magic' Configurations of Three-Qubit Observables and Geometric Hyperplanes of the Smallest Split Cayley Hexagon
• State Independent Proof of Kochen-Specker Theorem with Thirty Rank-Two Projectors
• Kochen-Specker Sets with a Mixture of 16 Rank-1 and 14 Rank-2 Projectors for a Three-Qubit System
• The many mathematical faces of Mermin's proof of the Kochen-Specker theorem
• A Class of Three-Qubit Contextual Configurations Located in Fano Pentads
• Vector Generation of Contextual Sets
• Generalized parity proofs of the Kochen-Specker theorem
• Nonclassical Structures within the N-qubit Pauli Group
• Construction of Three-Qubit Kochen-Specker Sets
• Arbitrarily large violations of non-contextuality in single mode photon states with positive Wigner function
• Veldkamp Spaces: From (Dynkin) Diagrams to (Pauli) Groups