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arXiv · 2210.06822

Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption

Kelvin Onggadinata·Dagomir Kaszlikowski·Pawel Kurzynski
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Abstract

The Kochen-Specker theorem states that exclusive and complete deterministic outcome assignments are impossible for certain sets of measurements, called Kochen-Specker (KS) sets. A straightforward consequence is that KS sets do not have joint probability distributions because no set of joint outcomes over such a distribution can be constructed. However, we show it is possible to construct a joint quasiprobability distribution over any KS set by relaxing the completeness assumption. Interestingly, completeness is still observable at the level of measurable marginal probability distributions. This suggests the observable completeness might not be a fundamental feature, but a secondary property.

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Kelvin Onggadinata, Dagomir Kaszlikowski, Pawel Kurzynski. 2022-10-13. Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption. https://doi.org/10.1103/physreva.107.022223

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