474 research outputs found
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
or , 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
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