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The Kochen-Specker theorem states that exclusive and complete deterministicoutcome assignments are impossible for certain sets of measurements, calledKochen-Specker (KS) sets. A straightforward consequence is that KS sets do nothave joint probability distributions because no set of joint outcomes over sucha distribution can be constructed. However, we show it is possible to constructa joint quasiprobability distribution over any KS set by relaxing thecompleteness assumption. Interestingly, completeness is still observable at thelevel of measurable marginal probability distributions. This suggests theobservable completeness might not be a fundamental feature, but a secondaryproperty.

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