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

Physical Review A

Which-way information in a nested Mach-Zehnder interferometer

Václav Potoček, Gergely Ferenczi

Published Aug 17, 2015• 41 citations
Publisher

Abstract

Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.

DOI
10.1103/physreva.92.023829

Related papers

One-state vector formalism for the evolution of a quantum state through nested Mach-Zehnder interferometers

Karol Bartkiewicz, Antonín Černoch, Dalibor Javůrek +3 more

Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.

arXiv:1410.8454•Physical Review A•Jan 12, 2015•39 citations

Paradox of photons disconnected trajectories being located by means of “weak measurements” in the nested Mach–Zehnder interferometer

G. N. Nikolaev

Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87 , 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111 , 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111 , 240402 (2013)] is unnecessary.

arXiv:1706.00662•Journal of Experimental and Theoretical Physics Letters•Feb 1, 2017•23 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 “Which-way information in a nested Mach-Zehnder interferometer”

Lev Vaidman A

Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi [Phys. Rev. A 92, 023829 (2015)] provided an analysis of the experimental evidence obtained by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] for the surprising behavior of photons passing through an interferometer, in particular, motion on disconnected paths. Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi reproduced the results of the experiment, but when analyzing its modification, they claimed that the reasoning of Danan et al., which led to disconnected paths, is erroneous. It is argued here that the criticism of Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi is unfounded.

arXiv:1509.02388•Physical Review A•Jan 26, 2016•27 citations

Comment on “One-state vector formalism for the evolution of a quantum state through nested Mach-Zehnder interferometers”

Lev Vaidman A

Bartkiewicz et al. [Phys. Rev. A 91, 012103 (2015)] provided an alternative analysis of an experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] which presented surprising evidence regarding the past of photons passing through an interferometer. They argued that the quantity used by Danan et al. is not a suitable which-path witness, and proposed an alternative. The weaknesses of the analysis are discussed, and it is argued that the alternative, analyzed properly, provides no new predictions.

arXiv:1508.07614•Physical Review A•Mar 31, 2016•24 citations

Interpreting a nested Mach-Zehnder interferometer with classical optics

Pablo L. Saldanha

In an recent work with the title ``Asking Photons Where They Have Been,'' Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013)]. In their words: ``The photons tell us that they have been in the parts of the interferometer through which they could not pass.'' They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.

arXiv:1312.7438•Physical Review A•Mar 13, 2014•42 citations
Recently, A. Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] performed a much-discussed experiment in which which-way information was obtained from the light in a nested Mach-Zehnder interferometer by weak measurement. The presented analysis using the two-state vector formalism drew the conclusions that the photons followed disconnected paths. We analyze this experiment using standard quantum optical methods and arrive at analytical expressions that match the experimental results without the need for such disconnected photon paths. We also propose a simple amendment to the experiment capable of displaying new phenomena, highlighting the advantages of our description.
Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.
Recently, a scheme based on the method of weak measurements to register the trajectories of photons passing through a nested Mach–Zehnder interferometer was proposed [L. Vaidman, Phys. Rev. A 87 , 052104 (2013)] and then realized [A. Danan, D. Farfurnik, S. Bar-Ad, et al., Phys. Rev. Lett. 111 , 240402 (2013)]. Interpreting the results of the experiment, the authors concluded that “the photons do not always follow continuous trajectories.” It is shown in this work that these results can be easily and clearly explained in terms of traditional classical electrodynamics or quantum mechanics implying the continuity of all possible paths of photons. Consequently, a new concept of disconnected trajectories proposed by the authors of work [Phys. Rev. Lett. 111 , 240402 (2013)] is unnecessary.
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.
Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi [Phys. Rev. A 92, 023829 (2015)] provided an analysis of the experimental evidence obtained by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] for the surprising behavior of photons passing through an interferometer, in particular, motion on disconnected paths. Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi reproduced the results of the experiment, but when analyzing its modification, they claimed that the reasoning of Danan et al., which led to disconnected paths, is erroneous. It is argued here that the criticism of Poto\ifmmode \check{c}\else \v{c}\fi{}ek and Ferenczi is unfounded.
Bartkiewicz et al. [Phys. Rev. A 91, 012103 (2015)] provided an alternative analysis of an experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013)] which presented surprising evidence regarding the past of photons passing through an interferometer. They argued that the quantity used by Danan et al. is not a suitable which-path witness, and proposed an alternative. The weaknesses of the analysis are discussed, and it is argued that the alternative, analyzed properly, provides no new predictions.
In an recent work with the title ``Asking Photons Where They Have Been,'' Danan et al. experimentally demonstrate an intriguing behavior of photons in an interferometer [Phys. Rev. Lett. 111, 240402 (2013)]. In their words: ``The photons tell us that they have been in the parts of the interferometer through which they could not pass.'' They interpret the results using the two-state vector formalism of quantum theory and say that, although an explanation of the experimental results in terms of classical electromagnetic waves in the interferometer is possible (and they provide a partial description), it is not so intuitive. Here we present a more detailed classical description of their experimental results, showing that it is actually intuitive. The same description is valid for the quantum wave function of the photons propagating in the interferometer. In particular, we show that it is essential that the wave propagates through all parts of the interferometer to describe the experimental results. We hope that our work helps to give a deeper understanding of these interesting experimental results.