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Weak values and the past of a quantum particle

Jonte R. Hance, JG Rarity, J Ladyman

Published Apr 21, 2023• 0 citations
Publisher

Abstract

We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle describes the state of a disturbed system, not that of a hypothetical undisturbed system. Second, even assuming no disturbance, there is no reason to associate the nonzero weak value of an operator containing the spatial projection operator with the classical idea of “particle presence.” Third, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic. Finally, weak value approaches to the path of a particle do not provide information beyond standard quantum mechanics (and the classical modes supporting the experiment). We know of no experiment with testable consequences that demonstrates a connection between particle presence and weak values.

DOI
10.25405/ncl.34496379

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Weak values and the past of a quantum particle

Jonte R. Hance, John Rarity, James Ladyman

We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle describes the state of a disturbed system, not that of a hypothetical undisturbed system. Second, even assuming no disturbance, there is no reason to associate the nonzero weak value of an operator containing the spatial projection operator with the classical idea of ``particle presence.'' Third, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic. Finally, weak value approaches to the path of a particle do not provide information beyond standard quantum mechanics (and the classical modes supporting the experiment). We know of no experiment with testable consequences that demonstrates a connection between particle presence and weak values.

arXiv:2109.14060•Physical Review Research•Apr 21, 2023•22 citations

Comment on "Does the weak trace show the past of a quantum particle?"

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In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time between preparation and detection. This conclusion relies on two arguments - (i) the role of the disturbance induced by a weak measurement, and (ii) classical-like features like continuous paths that must purportedly be associated with a quantum particle presence. Here we first show that (i) arises from a misunderstanding of null weak values by putting forward a simple counter-example that highlights that the relevant quantities to examine are the vanishing amplitudes, not the wavefunction. Then we briefly argue that enforcing classical pre-conditions in order to account for quantum properties during unitary evolution is unlikely to lead to a consistent understanding of quantum phenomena.

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Reply to “Comment on ‘Weak values and the past of a quantum particle' ”

Jonte R. Hance, John Rarity, James Ladyman

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.

arXiv:2309.07599•Physical Review Research•Nov 8, 2023•4 citations

Reply to “Comment on ‘Weak values and the past of a quantum particle' ”

Jonte R. Hance, JG Rarity, J Ladyman

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.

•Nov 8, 2023•0 citations
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle describes the state of a disturbed system, not that of a hypothetical undisturbed system. Second, even assuming no disturbance, there is no reason to associate the nonzero weak value of an operator containing the spatial projection operator with the classical idea of “particle presence.” Third, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic. Finally, weak value approaches to the path of a particle do not provide information beyond standard quantum mechanics (and the classical modes supporting the experiment). We know of no experiment with testable consequences that demonstrates a connection between particle presence and weak values.
We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle describes the state of a disturbed system, not that of a hypothetical undisturbed system. Second, even assuming no disturbance, there is no reason to associate the nonzero weak value of an operator containing the spatial projection operator with the classical idea of ``particle presence.'' Third, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic. Finally, weak value approaches to the path of a particle do not provide information beyond standard quantum mechanics (and the classical modes supporting the experiment). We know of no experiment with testable consequences that demonstrates a connection between particle presence and weak values.
In the paper "Does the weak trace show the past of a quantum particle?" [arXiv:2109.14060v2], it is argued that null weak values of the spatial projectors are inadequate to infer the presence of a quantum particle at an intermediate time between preparation and detection. This conclusion relies on two arguments - (i) the role of the disturbance induced by a weak measurement, and (ii) classical-like features like continuous paths that must purportedly be associated with a quantum particle presence. Here we first show that (i) arises from a misunderstanding of null weak values by putting forward a simple counter-example that highlights that the relevant quantities to examine are the vanishing amplitudes, not the wavefunction. Then we briefly argue that enforcing classical pre-conditions in order to account for quantum properties during unitary evolution is unlikely to lead to a consistent understanding of quantum phenomena.
Nondestructive weak measurements (WMs) made on a quantum particle are useful in order to extract information as the particle evolves from a prepared state to a finally detected state. The physical meaning of this information has been open to debate, particularly in view of the apparent discontinuous trajectories of the particle recorded by WMs. In this work we investigate the properties of vanishing weak values for projection operators as well as general observables. We then analyze the implications when inferring the past of a quantum particle. We provide a nonoptical example for which apparent discontinuous trajectories are obtained by WMs. Our approach is compared to previous results.
We investigate the weak trace method for determining the path of a quantum particle in an unperturbed system. Specifically, looking at nested interferometer experiments, when internal interferometers are tuned to destructive interference, we show that the weak trace method gives misleading results. This is because the methods used experimentally to obtain the weak value of the position operator necessarily perturb the system, hence, in some cases the assumption that weak coupling being equivalent to no coupling is incorrect. Experiments performed that are claimed to support the interpretation simply show the effects of this coupling acting as measurement, rather than tapping into the underlying reality of what happens in a quantum system when no-one is looking.
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.