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arXiv:1607.03498 · Physics Letters A

Revisiting the admissibility of non-contextual hidden variable models in quantum mechanics

Atul Singh Arora, Kishor Bharti, Arvind

Published Nov 30, 2018• 3 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2018.11.049

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We propose a non-contextual hidden variable model, consistent with all predictions of quantum mechanics (QM). A careful scrutiny of consistency requirements of any hidden variable model with quantum mechanics and the corresponding no-go theorems, leads us to the conclusion that the notion of contextuality is not a necessary feature of QM. The alternative view that emerges, hinges on identifying a new classical property which we call multiplicativity. It turns out that by relaxing this condition of multiplicativity on hidden variable models, they can be made consistent with QM. The connection of non-multiplicativity to Bohm's model and to apparent contextuality is also discussed.
No physical measurement can be performed with infinite precision. This leaves a loophole in the standard no–go arguments against non–contextual hidden variables. All such arguments rely on choosing special sets of quantum–mechanical observables with measurement outcomes that cannot be simulated non–contextually. As a consequence, these arguments do not exclude the hypothesis that the class of physical measurements in fact corresponds to a dense subset of all theoretically possible measurements with outcomes and quantum probabilities that can be recovered from a non–contextual hidden–variable model. We show here by explicit construction that there are indeed such non–contextual hidden–variable models, both for projection–valued and positive–operator–valued measurements.