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

TL;DR

This paper demonstrates that by relaxing the completeness assumption, one can construct joint quasiprobability distributions over Kochen-Specker sets, challenging the notion that observable completeness is fundamental.

Contribution

It introduces a method to construct joint quasiprobability distributions over KS sets by relaxing the completeness assumption, offering new insights into the nature of observable completeness.

Findings

Joint quasiprobability distributions can be constructed over KS sets.

Observable marginal distributions still exhibit completeness.

Completeness may be a secondary, not fundamental, property.

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.