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

TL;DR

This paper demonstrates that logical pre- and post-selection paradoxes in quantum mechanics are direct proofs of contextuality, especially when involving strong measurements, highlighting the fundamental role of measurement disturbance and specific conditions.

Contribution

It establishes that strong measurement versions of these paradoxes directly manifest quantum contextuality, clarifying the conditions under which contextuality can be proven.

Findings

Strong measurements reveal direct contextuality evidence

Luders-von Neumann updates are essential for proving contextuality

Anomalous weak values also indicate contextuality

Abstract

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 Luders-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 Luders-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.