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 the impossibility of a noncontextual hidden variable theory. This proof is obtained by considering all the measurements involved in the paradoxical effect—the preselection, the post-selection, and the alternative possible intermediate measurements—as alternative possible measurements at a single time.
Leifer, M.S., Spekkens, R.W., 2005. Pre- and Post-Selection Paradoxes and Contextuality in Quantum Mechanics. Phys. Rev. Lett. 95, 200405. doi:10.1103/PhysRevLett.95.200405
American Physical Society