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arXiv:1312.7566 · Physical Review A

Tracing the past of a quantum particle

Lev Vaidman A

Published Feb 13, 2014• 64 citations
arXivHTMLPDF

Abstract

The question ``Where was a quantum particle between pre- and postselection measurements?'' is analyzed in view of a recent proposal that the quantum particle was in the overlap of the forward and backward evolving wave functions. It is argued that this proposal corresponds not only to the criterion of where the particle leaves a weak trace but also to the criterion of where the local interactions can affect the probability of postselection and where finding the particle in a strong nondemolition measurement is possible. The concept of a ``secondary presence'' of a pre- and postselected particle where local interactions affect the weak trace in the overlap region is introduced.

DOI
10.1103/physreva.89.024102

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Physical Review A•Oct 29, 2013•65 citations
The question Where was a quantum particle between pre- and postselection measurements?'' is analyzed in view of a recent proposal that the quantum particle was in the overlap of the forward and backward evolving wave functions. It is argued that this proposal corresponds not only to the criterion of where the particle leaves a weak trace but also to the criterion of where the local interactions can affect the probability of postselection and where finding the particle in a strong nondemolition measurement is possible. The concept of a secondary presence'' of a pre- and postselected particle where local interactions affect the weak trace in the overlap region is introduced.
Although there is no consensus regarding the ``reality'' of the past of a quantum particle, in situations where there is only one trajectory with a nonvanishing quantum wave of the particle between its emission and detection points, it seems ``safe'' to associate the past of the particle with this trajectory. A method for analyzing the past of a quantum particle according to the weak trace it leaves is proposed. Such a trace can be observed via measurements performed on an ensemble of identically pre- and postselected particles. Examples in which this method contradicts the above common sense description of the past of the particle are presented. It is argued that it is possible to describe the past of a quantum particle, but the naive approach has to be replaced by both forward- and backward-evolving quantum states.
Vaidman has proposed a controversial criterion for determining the past of a single quantum particle based on the “weak trace” it leaves. We here consider more general examples of entangled systems and analyze the past of single, as well as pairs of entangled pre- and postselected particles. Systems with nontrivial time evolution are also analyzed. We argue that in these cases, examining only the single-particle weak trace provides information which is insufficient for understanding the system as a whole. We therefore suggest to examine, alongside with the past of single particles, also the past of pairs, triplets and eventually the entire system, including higher-order, multipartite traces in the analysis. This resonates with a recently proposed top-down approach by Aharonov, Cohen and Tollaksen for understanding the structure of correlations in pre- and postselected systems.
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.
An approach for analysis of effective interaction between pre- and postselected quantum particles is developed. It is argued that the cases of complete pre- and postselection of particles are more profound than the cases of partial pre- and postselection, since the former goes beyond modification of the average of interactions on an ensemble of experiments. Recently discussed paradoxical phenomena such as the pigeonhole paradox and the modification of the interaction from repulsion to attraction are analyzed within the introduced formalism, and a few new surprising examples are presented.