A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
arXiv:1505.02603 · doi:10.1088/1367-2630/17/9/093001
Abstract
Quantum contextuality is one of the fundamental notions in quantum mechanics. Proofs of the Kochen-Specker theorem and noncontextuality inequalities are two means for revealing the contextuality phenomenon in quantum mechanics. It has been found that some proofs of the Kochen-Specker theorem, such as those based on rays, can be converted to a state-independent noncontextuality inequality, but it remains open whether it is true in general, i.e., whether any proof of the Kochen-Specker theorem can always be converted to a noncontextuality inequality. In this paper, we address this issue. We prove that all kinds of proofs of the Kochen-Specker theorem, based on rays or any other observables, can always be converted to state-independent noncontextuality inequalities. Besides, our constructive proof also provides a general approach for deriving a state-independent noncontextuality inequality from a proof of the Kochen-Specker theorem.
10 pages, no figure
References in corpus (12)
- Contextuality supplies the magic for quantum computation
- A simple test for hidden variables in spin-1 system
- Experimentally testable state-independent quantum contextuality
- Wigner function negativity and contextuality in quantum computation on rebits
- Universality of state-independent violation of correlation inequalities for noncontextual theories
- Proposed experiment for testing quantum contextuality with neutrons
- Applying the simplest Kochen-Specker set for quantum information processing
- Greenberger-Horne-Zeilinger paradoxes from qudit graph states
- On small proofs of Bell-Kochen-Specker theorem for two, three and four qubits
- Experimental observation of impossible-to-beat quantum advantage on a hybrid photonic system
- Coexistence of Kochen-Specker inequalities and noncontextuality inequalities
- Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities
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- Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
- Algebraic structures identified with bivalent and non-bivalent semantics of experimental quantum propositions