Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1704.03722 · Physical Review A

Past of a quantum particle revisited

Berthold‐Georg Englert, Kelvin Horia, Jibo Dai, Yink Loong Len, Hui Khoon Ng

Published Aug 21, 2017• 53 citations
arXivHTMLPDF

Abstract

We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.

DOI
10.1103/physreva.96.022126

Related papers

Unambiguous path discrimination in a two-path interferometer

Yink Loong Len, Jibo Dai, Berthold‐Georg Englert +1 more

When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon (``signal'') through a Mach-Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon (``idler'') whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer cannot be known; and every photon that emerges from the dark output port of the balanced interferometer has a known path.

arXiv:1708.01408•Physical Review A•Aug 7, 2018•12 citations

Particle path through a nested Mach-Zehnder interferometer

Robert B. Griffiths

Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [Phys. Rev. A 87, 052104 (2013)], and agree with a conclusion reached by Li et al. [Phys. Rev. A 88, 046102 (2013)]. However, the analysis casts serious doubt on the claim of Salih et al. (whose authorship includes Li et al.) [Phys. Rev. Lett. 110, 170502 (2013)] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.

arXiv:1604.04596•Physical Review A•Sep 16, 2016•79 citations

Comment on “Past of a quantum particle revisited”

Uri Peleg, Lev Vaidman A

The recent criticism of Vaidman's proposal for the analysis of the past of a particle in the nested interferometer is refuted. It is shown that the definition of the past of the particle adopted by Englert et al. [B. G. Englert et al., Phys. Rev. A 96, 022126 (2017)] is applicable only to a tiny fraction of photons in the interferometer which indeed exhibit different behavior. Their proof that all pre- and postselected particles behave this way, i.e., follow a continuous trajectory, does not hold, because it relies on the assumption that it is intended to prove.

arXiv:1805.12171•Physical Review A•Feb 27, 2019•36 citations

Asking Photons "Where Have They Been?"

Lev Vaidman A

Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a ``common sense'' approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting•Jan 1, 2013•6 citations

Asking photons where have they been

Danan, Ariel, Demitry Farfurnik, Shimshon Bar-Ad +1 more

Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.

arXiv:1304.7469•Apr 28, 2013•1 citation

Where is the photon in an interferometer?

J. E. Avron

In a paper titled "Asking photons where they have been?" \cite{LV} Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors. They argue that the experiment supports Aharonov-Vaidman's formulation of quantum mechanics \cite{AharonovVaidman} where post-selected particles are assigned disconnected trajectories. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The standard view of interfering trajectories accounts for the experimental findings.

arXiv:2007.03624•Jul 7, 2020•0 citations
We analyze Vaidman's three-path interferometer with weak path marking [L. Vaidman, Phys. Rev. A 87, 052104 (2013)] and find that common sense yields correct statements about the particle's path through the interferometer. This disagrees with the original claim that the particles have discontinuous trajectories at odds with common sense. In our analysis, ``the particle's path'' has operational meaning as acquired by a path-discriminating measurement. For a quantum-mechanical experimental demonstration of the case, one should perform a single-photon version of the experiment by Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] with unambiguous path discrimination. We present a detailed proposal for such an experiment.
When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon (``signal'') through a Mach-Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon (``idler'') whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer cannot be known; and every photon that emerges from the dark output port of the balanced interferometer has a known path.
Possible paths of a photon passing through a nested Mach-Zehnder interferometer on its way to a detector are analyzed using the consistent histories formulation of quantum mechanics, and confirmed using a set of weak measurements (but not weak values). The results disagree with an analysis by Vaidman [Phys. Rev. A 87, 052104 (2013)], and agree with a conclusion reached by Li et al. [Phys. Rev. A 88, 046102 (2013)]. However, the analysis casts serious doubt on the claim of Salih et al. (whose authorship includes Li et al.) [Phys. Rev. Lett. 110, 170502 (2013)] to have constructed a protocol for counterfactual communication: a channel which can transmit information even though it contains a negligible number of photons.
The recent criticism of Vaidman's proposal for the analysis of the past of a particle in the nested interferometer is refuted. It is shown that the definition of the past of the particle adopted by Englert et al. [B. G. Englert et al., Phys. Rev. A 96, 022126 (2017)] is applicable only to a tiny fraction of photons in the interferometer which indeed exhibit different behavior. Their proof that all pre- and postselected particles behave this way, i.e., follow a continuous trajectory, does not hold, because it relies on the assumption that it is intended to prove.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a ``common sense'' approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
Quantum mechanics does not provide a clear answer to the question: What was the past of a photon which went through an interferometer? Various welcher weg measurements, delayed-choice which-path experiments and weak-measurements of photons in interferometers presented the past of a photon as a trajectory or a set of trajectories. We have carried out experimental weak measurements of the paths of photons going through a nested Mach-Zehnder interferometer which show a different picture: the past of a photon is not a set of continuous trajectories. The photons tell us that they have been in the parts of the interferometer which they could not have possibly reached! Our results lead to rejection of a "common sense" approach to the past of a quantum particle. On the other hand, they have a simple explanation within the framework of the two-state vector formalism of quantum theory.
In a paper titled "Asking photons where they have been?" \cite{LV} Danan, Farfurnik, Bar-Ad and Vaidman describe an experiment with pre and post selected photons going through nested Mach-Zehnder interferometers. They find that some of the mirrors leave no footprints on the signal and interpret this as evidence that the photon skipped these mirrors. They argue that the experiment supports Aharonov-Vaidman's formulation of quantum mechanics \cite{AharonovVaidman} where post-selected particles are assigned disconnected trajectories. I review the experiment and analyze it within the orthodox framework of quantum mechanics. The standard view of interfering trajectories accounts for the experimental findings.