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Pre- and Post-selection paradoxes and contextuality in quantum mechanics

M. S. Leifer·R. W. Spekkens
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Abstract

Many seemingly paradoxical effects are known in the predictions for outcomes of intermediate measurements made on pre- and post-selected quantum systems. Despite appearances, these effects do not demonstrate the impossibility of a noncontextual hidden variable theory, since an explanation in terms of measurement-disturbance is possible. Nonetheless, we show that for every paradoxical effect wherein all the pre- and post- selected probabilities are 0 or 1 and the pre- and post-selected states are nonorthogonal, there is an associated proof of contextuality. This proof is obtained by considering all the measurements involved in the paradoxical effect -- the pre-selection, the post-selection, and the alternative possible intermediate measurements -- as alternative possible measurements at a single time.

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M. S. Leifer, R. W. Spekkens. 2005-07-06. Pre- and Post-selection paradoxes and contextuality in quantum mechanics. https://doi.org/10.1103/physrevlett.95.200405

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