The measurement paradox

Jeff S. Lundeen, Aephraim M. Steinberg

It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.

Lars‐Göran Johansson

Clifford Alan Hooker

Once upon a time the well-known paradoxes of quantum mechanics (one might even say the “traditional” paradoxes of quantum mechanics!—I refer here to paradoxes such as the Schrödinger cat and the Einstein-Podolsky-Rosen Paradox) seemed especially difficult because of the rather bizarre behavior of the wave packet under the von Neumann theory of measurement, to which behavior these paradoxical situations seemed to draw especial attention. Quite recently quantum theoretical accounts of the measurement process have been appearing which sidestep direct reference to such things as “contraction” of the wave packet (see, for example, Krips and Jauch). With this development it has become increasingly popular to take a “cool” approach to these paradoxes, arguing that the new approach to measurement provides a consistent, nonbizarre account of the physical situations and that the paradoxicality was due largely to intuitive blunders—even plausible intuitive blunders—accentuated (but also disguised) by the unfortunate features of the von Neumann approach to measurement. Both Krips and Jauch, for example, adopt this approach.

Josh Roeloffs

Detlef Dürr, Dustin Lazarovici

Matthew F. Pusey, Matthew Leifer

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.