Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical variables have their values defined even when they cannot be measured.
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A nondispersive dynamical variable is not necessarily a proper dynamical variable. The latter should be used as the requirement for hidden variable underpinning whenever distinction arises.
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Revzen, M. The Wigner Function as Distribution Function. Found Phys 36, 546–562 (2006). https://doi.org/10.1007/s10701-005-9037-5
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DOI: https://doi.org/10.1007/s10701-005-9037-5