Isomorphism between the Peres and Penrose proofs of the BKS theorem in three dimensions
arXiv:0909.4502 · doi:10.1007/s10701-010-9434-2
Abstract
It is shown that the 33 complex rays in three dimensions used by Penrose to prove the Bell-Kochen-Specker theorem have the same orthogonality relations as the 33 real rays of Peres, and therefore provide an isomorphic proof of the theorem. It is further shown that the Peres and Penrose rays are just two members of a continuous three-parameter family of unitarily inequivalent rays that prove the theorem.
7 pages, 2 Tables. A concluding para and 9 new references have been added to the second version
References in corpus (6)
- State-independent experimental test of quantum contextuality
- Experimental test of quantum contextuality in neutron interferometry
- State-independent quantum contextuality with single photons
- Preparation contextuality powers parity-oblivious multiplexing
- Universality of state-independent violation of correlation inequalities for noncontextual theories
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Cited by in corpus (8)
- Kochen-Specker Contextuality
- Converting contextuality into nonlocality
- Arbitrarily exhaustive hypergraph generation of 4-, 6-, 8-, 16-, and 32-dimensional quantum contextual sets
- Certifying sets of quantum observables with any full-rank state
- Simplest bipartite perfect quantum strategies
- The simplest Kochen-Specker set
- 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