Reexamination of the Kochen-Specker theorem: Relaxation of the completeness assumption
arXiv:2210.06822 · doi:10.1103/PhysRevA.107.022223
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.
5 pages, 1 figure
References in corpus (8)
- A simple test for hidden variables in spin-1 system
- Experimentally testable state-independent quantum contextuality
- State-independent experimental test of quantum contextuality
- Kochen-Specker Contextuality
- Framed Hilbert space: hanging the quasi-probability pictures of quantum theory
- Significant-loophole-free test of Kochen-Specker contextuality using two species of atomic-ions
- Exploring non-signalling polytopes with negative probability
- Witnessing Bell violations through probabilistic negativity