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arXiv:1407.4613

Weak measurement criteria for the past of a quantum particle

B. E. Y. Svensson

Published Jul 17, 2014• 1 citation
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Abstract

Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose instead a weak mean value criterion which avoids these shortcomings.

DOI
10.48550/arxiv.1407.4613

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We here reply to a recent comment by Vaidman [Phys. Rev. Res. 5, 048001 (2023)] on our paper [Phys. Rev. Res. 5, 023048 (2023)]. In his Comment, Vaidman first admits that he is just defining (assuming) the weak trace gives the presence of a particle—however, in this case, he should use a term other than presence, as this already has a separate, intuitive meaning other than “where a weak trace is.” Despite this admission, Vaidman then goes on to argue for this definition by appeal to ideas around an objectively existing idea of presence. We show these appeals rely on their own conclusion—that there is always a matter of fact about the location of a quantum particle.

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I provide additional arguments for refuting Vaidmans weak value analysis of the path of a particle in a nested Mach-Zehnder interferometer. The argument uses sequential weak values to supplement my previous analysis according to which even weak measurements disturb the system to such an extent that projector weak values cannot be considered representative for the undisturbed system.

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Vaidman, Phys.Rev. A 87, 052104 (2013), has proposed a weak value criterion for the past of a quantum particle, and applied it to photons in a particular setup of nested Mach-Zehnder interferometers. From his analysis, he draws some astonishing conclusions regarding which arms of the setup the photons populate. I argue that the weak values Vaidman employs as weak tracers in his analysis cannot be used in this case and that, consequently, the conclusions he draws cannot be upheld. The reason is that weak values are defined as a limit which in this case turns out to be discontinuous. I propose instead a weak mean value criterion which avoids these shortcomings.
We here reply to a recent comment by Vaidman [Phys. Rev. Res. 5, 048001 (2023)] on our paper [Phys. Rev. Res. 5, 023048 (2023)]. In his Comment, Vaidman first admits that he is just defining (assuming) the weak trace gives the presence of a particle—however, in this case, he should use a term other than presence, as this already has a separate, intuitive meaning other than “where a weak trace is.” Despite this admission, Vaidman then goes on to argue for this definition by appeal to ideas around an objectively existing idea of presence. We show these appeals rely on their own conclusion—that there is always a matter of fact about the location of a quantum particle.
We here reply to a recent comment by Vaidman [Phys. Rev. Res. 5, 048001 (2023)] on our paper [Phys. Rev. Res. 5, 023048 (2023)]. In his Comment, Vaidman first admits that he is just defining (assuming) the weak trace gives the presence of a particle---however, in this case, he should use a term other than presence, as this already has a separate, intuitive meaning other than ``where a weak trace is.'' Despite this admission, Vaidman then goes on to argue for this definition by appeal to ideas around an objectively existing idea of presence. We show these appeals rely on their own conclusion---that there is always a matter of fact about the location of a quantum particle.