Logical pre- and post-selection paradoxes are proofs of contextuality

• Published in: Electronic proceedings in theoretical computer science Vol. 195; no. Proc. QPL 2015; pp. 295 - 306
• Main Authors: Pusey, Matthew F., Leifer, Matthew S.
• Format: Journal Article
• Language: English
• Published: Open Publishing Association 04.11.2015
• ISSN: 2075-2180; 2075-2180
• DOI: 10.4204/EPTCS.195.22

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 [quant-ph/0412178] identified a striking class of such paradoxes, known as logical pre- and post-selection 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 [arXiv:1409.1535], we now know that this is true for both realizations of logical pre- and post-selection paradoxes.