Bypassing the Kochen-Specker theorem: an explicit non-contextual statistical model for the qutrit

We present an explicit non-contextual model of hidden variables for the qutrit. The model consists of an infinite set of possible hidden configurations uniformly distributed over a sphere, each one having a well-defined probability density to happen and a well-defined non-contextual binary outcome, either $+1$ or $-1$, for every properly formulated test. The model reproduces the predictions of quantum mechanics and, thus, it bypasses the constraints imposed by the Kochen-Specker theorem and its subsequent reformulations. The crux of the model is the observation that all these theorems crucially rely on an implicit assumption that is not actually required by fundamental physical principles, namely, the existence of an absolute frame of reference with respect to which the polarization properties of the qutrit as well as the orientation of the tests performed on it can be defined. We notice, on the other hand, that pairs of compatible tests defined in such an hypothetical absolute frame of reference that can be obtained from each other through a global rotation that leaves the state of the qutrit unchanged would by physically undistinguishable and, hence, equivalent under a gauge symmetry transformation. This spurious gauge degree of freedom must be properly fixed in order to build the statistical model for the qutrit. In two previous papers we have shown that the same implicit assumption is also required in order to prove both Bell's theorem and the Greenberger-Horne-Zeilinger theorem