Coexistence of Kochen-Specker inequalities and noncontextuality inequalities
arXiv:1402.5200 · doi:10.1103/PhysRevA.89.010101
Abstract
Two types of inequalities, Kochen-Specker inequalities and noncontextuality inequalities, are both used to demonstrate the incompatibility between the noncontextual hidden variable model and quantum mechanics. It has been thought that noncontextuality inequalities are much more potent than Kochen-Specker inequalities, since the latter are constrained by the Kochen-Specker rules, which are regarded as an extra constraint imposed on the noncontextual hidden variable model. However, we find that a noncontextuality inequality exists in a ray set if and only if a Kochen-Specker inequality exists in the same ray set. This provides an effect approach both for constructing noncontextuality inequalities in a Kochen-Specker set and for converting a Kochen-Specker inequality to a noncontextuality inequality in any ray set.
5 pages
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Cited by in corpus (8)
- Kochen-Specker Contextuality
- A variant of the Kochen-Specker theorem localising value indefiniteness
- Necessary and sufficient condition for quantum state-independent contextuality
- Quantum Contextuality
- A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality
- Demonstrating quantum contextuality of indistinguishable particles by a single family of noncontextuality inequalities
- Characterizing high-dimensional quantum contextuality
- Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions