If a quantum system is prepared and later post-selected in certain states, “paradoxical” predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective measurement with Lüders-von Neumann update rule, or with weak measurements where they show up in anomalous weak values. Leifer and Spekkens [Phys. Rev. Lett. 95, 200405] identified a striking class of such paradoxes, known as logical pre- and postselection paradoxes, and showed that they are indirectly connected with contextuality. By analysing the measurement-disturbance required in models of these phenomena, we find that the strong measurement version of logical pre- and post-selection paradoxes actually constitute a direct manifestation of quantum contextuality. The proof hinges on under-appreciated features of the paradoxes. In particular, we show by example that it is not possible to prove contextuality without Lüders-von Neumann updates for the intermediate measurements, nonorthogonal pre- and post-selection, and 0/1 probabilities for the intermediate measurements. Since one of us has recently shown that anomalous weak values are also a direct manifestation of contextuality [Phys. Rev. Lett. 113, 200401], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.
Pusey, M.F., Leifer, M.S. 2015. Logical pre- and post-selection paradoxes are proofs of contextuality. Proc. 12th International Workshop on Quantum Physicsand Logic (QPL2015).
Later appeared in Electronic Proceedings in Theoretical Computer Science, vol. 195, edited by C. Heunen, P. Selinger and J. Vicary, pp. 295-306.