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arXiv · 1505.02603

A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality

Xiao-Dong Yu·Yan-Qing Guo·D. M. Tong
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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.

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Xiao-Dong Yu, Yan-Qing Guo, D. M. Tong. 2015-05-11. A proof of the Kochen-Specker theorem can always be converted to a state-independent noncontextuality inequality. https://doi.org/10.1088/1367-2630%2F17%2F9%2F093001

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