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arXiv:quant-ph/0412179 · International Journal of Theoretical Physics

Logical Pre- and Post-Selection Paradoxes, Measurement-Disturbance and Contextuality

Matthew Leifer, Robert W. Spekkens

Published Nov 1, 2005• 23 citations
arXivHTMLPDF
DOI
10.1007/s10773-005-8975-1

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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.
By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre- and post-selection (i.e. weak measurements), then novel experimental aspects of contextuality can be demonstrated including a proof that every PPS-paradox with definite predictions implies contextuality. Certain results of these measurements (eccentric weak values with e.g. negative values outside the spectrum), however, cannot be explained by a classical-like hidden variable theory. Surprising theoretical implications are discussed.
By analyzing the concept of contextuality (Bell-Kochen-Specker) in terms of pre-and-post-selection (PPS), it is possible to assign definite values to observables in a new way. Physical reasons are presented for restrictions on these assignments. When measurements are performed which do not disturb the pre- and post-selection (i.e. weak measurements), then novel experimental aspects of contextuality can be demonstrated including a proof that every PPS-paradox with definite predictions implies contextuality. Certain results of these measurements (eccentric weak values with e.g. negative values outside the spectrum), however, cannot be explained by a "classical-like" hidden variable theory. Surprising theoretical implications are discussed.