On Noncontextual, Non-Kolmogorovian Hidden Variable Theories



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PIRSA Number: 
16010073

Abstract

One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space.  Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms.  We present a theorem to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of possibilities.  This serves as a kind of "no-go" theorem for these alternative, or generalized, probability theories.