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No 'anomalous' weak values in a classical theory

D. Sokolovski

Published Oct 2, 2014• 0 citations
OpenAlex

Abstract

The authors of a recent paper [Phys. Rev. Lett. 113, 120404 (2014)] suggest that weak values are not inherently quantum but rather a purely statistical feature of pre- and postselection with disturbance. We argue that this claim is erroneous, since such values require averaging with distributions which change sign. This type of averaging arises naturally in quantum mechanics, but may not occur in classical statistics.

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A comment on the paper "How can a Result of a Single Coin Toss Turn Out to be 100 Heads" by C. Ferrie and J. Combes

D. Sokolovski

The authors of a recent paper [Phys. Rev. Lett. 113, 120404 (2014)] suggest that "weak values are not inherently quantum but rather a purely statistical feature of pre- and postselection with disturbance". We argue that this claim is erroneous, since such values require averaging with distributions which change sign. This type of averaging arises naturally in quantum mechanics, but may not occur in classical statistics.

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Weak values as interference phenomena

Justin Dressel

Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement. These averages can exceed the eigenvalue range of the observable ostensibly being estimated, which has prompted considerable debate regarding their interpretation. Classical conditioned averages of noisy signals only show such anomalies if the quantity being measured is also disturbed prior to conditioning. This fact has recently been rediscovered, along with the question whether anomalous weak values are merely classical disturbance effects. Here we carefully review the role of the weak value as both a conditioned observable estimation and a dynamical variable, and clarify why classical disturbance models will be insufficient to explain the weak value unless they can also simulate other quantum interference phenomena.

arXiv:1410.0943•Physical Review A•Mar 18, 2015•127 citations
The authors of a recent paper [Phys. Rev. Lett. 113, 120404 (2014)] suggest that weak values are not inherently quantum but rather a purely statistical feature of pre- and postselection with disturbance. We argue that this claim is erroneous, since such values require averaging with distributions which change sign. This type of averaging arises naturally in quantum mechanics, but may not occur in classical statistics.
The average result of a weak measurement of some observable A can, under postselection of the measured quantum system, exceed the largest eigenvalue of A. The nature of weak measurements, as well as the presence of postselection and hence possible contribution of measurement disturbance, has led to a long-running debate about whether or not this is surprising. Here, it is shown that such "anomalous weak values" are nonclassical in a precise sense: a sufficiently weak measurement of one constitutes a proof of contextuality. This clarifies, for example, which features must be present (and in an experiment, verified) to demonstrate an effect with no satisfying classical explanation.
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.
The question of what is genuinely quantum about weak values is only ever going to elicit strongly subjective opinions---it is not a scientific question. Good questions, when comparing theories, are operational---they deal with the unquestionable outcomes of experiment. We give the anomalous shift of weak values an objective meaning through a generalization to an operational definition of anomalous post-selected averages. We show the presence of these averages necessitate correlations in every model giving rise to them---quantum or classical. Characterizing such correlations shows that they are ubiquitous. We present the simplest classical example without the need of disturbance realizing these generalized anomalous weak values.
Weak values arise experimentally as conditioned averages of weak (noisy) observable measurements that minimally disturb an initial quantum state, and also as dynamical variables for reduced quantum state evolution even in the absence of measurement. These averages can exceed the eigenvalue range of the observable ostensibly being estimated, which has prompted considerable debate regarding their interpretation. Classical conditioned averages of noisy signals only show such anomalies if the quantity being measured is also disturbed prior to conditioning. This fact has recently been rediscovered, along with the question whether anomalous weak values are merely classical disturbance effects. Here we carefully review the role of the weak value as both a conditioned observable estimation and a dynamical variable, and clarify why classical disturbance models will be insufficient to explain the weak value unless they can also simulate other quantum interference phenomena.