Probabilistic Generation of Quantum Contextual Sets

Abstract

We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these sets, and it gives all sets while the parity proof method gives only sets with an odd number of edges in their hypergraph representation. Thus we obtain 35 new kinds of critical KS sets with an even number of edges. Using a random sample of the sets generated with our method, we give a statistical estimate of the number of sets that might be obtained in an eventual exhaustive enumeration.

22 pages, 7 figures

References in corpus (9)

• Multi-party entanglement in graph states
• State-independent experimental test of quantum contextuality
• Experimental test of quantum contextuality in neutron interferometry
• State-independent quantum contextuality with single photons
• Proposed experiment for testing quantum contextuality with neutrons
• Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
• Graph Approach to Quantum Systems
• Estimating Bernoulli trial probability from a small sample
• All-versus-nothing proofs with n qubits distributed between m parties

Cited by in corpus (14)

• Kochen-Specker Contextuality
• 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
• 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
• Automated generation of Kochen-Specker sets
• The Minimum Complexity of Kochen-Specker Sets Does Not Scale with Dimension
• Hypergraph Contextuality
• Estimating Bernoulli trial probability from a small sample
• New Examples of Kochen-Specker Type Configurations on Three Qubits
• Vector Generation of Contextual Sets
• Non-Kochen-Specker Contextuality
• Nonclassical Structures within the N-qubit Pauli Group
• Multisetting Bell inequalities for $N$ spins-1 avoiding KS contradiction