Delayed Choice for Entangled Photons

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review Manuscript “Delayed choice for entangled photons”, ID: photonics-3665751

The paper “Delayed choice for entangled photons” presents a delayed choice experiment in the well-known setup of a Mach-Zehnder interferometer (MZI). While the paper contains novel and interesting ideas, it requires extensive review before publication. Below, I outline my main concerns, along with some constructive suggestions.

Major Comments

The manuscript (MS) overemphasizes the role of the apparent contradiction between the wave-like and particle-like properties of the photon. This tone appears from the beginning of the MS. For example, line 8 (L8) in the abstract: “We show that this contradiction can be resolved”, L25: “This paradox suggests…”, L91: “It is complicated to resolve this apparent paradox…”. However, this reviewer finds it difficult to understand the existence of a paradox or contradiction when we have a theoretical framework (Quantum Mechanics) that addresses all experimental contexts and has not presented any experimental falsification to date. In this sense, the MS states that the main aspects are state preparation and measurement (collapse). Furthermore, in the MS, the full quantum formalism is used to analyze their experimental context. So, how can we understand the nature of the contradiction or paradox if we have a theoretical formalism that answers correctly all our experimental questions? Citing Feynman [Lectures on Physics, Vol III, Ch. 18]:
Do you still think there is a “paradox”? Make sure that it is, in fact, a paradox about the behavior of Nature, by setting up an imaginary experiment for which the theory of quantum mechanics would predict inconsistent results via two different arguments. Otherwise, the “paradox” is only a conflict between reality and your feeling of what reality “ought to be.”

Due to this lack of conceptual precision, the MS presents confusing or imprecise ideas. For example, in L 74-79, the MS stated “To date, we lack wave detectors…”, which is correct, to follow: “This is equivalent to stating that we do not have detectors for probability amplitudes C, but only ones that measure probabilities |C|². Our detectors measure probabilities. The only way to observe these two wave components is to bring them together simultaneously, completing an interferometer”. In this sentence, we have a true antecedent “we can only measure the squared amplitudes", because the amplitudes are complex numbers but an imprecise conclusion “the only way to observe the two components is by using the interferometer”. Utilizing a Hanbury Brown and Twiss (HBT) scheme, used in section 2, we know that a single photon state (particle-like) exhibits anti-correlations, i.e., detectors D2 and D3 (Figure 1) never detect simultaneously, and a coherent state exhibits perfect correlations, i.e., D2 and D3 always detect simultaneously. In other words, we can simultaneously measure the two squared amplitudes with the HBT, while with the MZI, we can measure the phase between the two components. This reviewer believes that a work focused on the "foundations of quantum theory" requires clarity and conceptual precision, with logical rigor of argumentation. This manuscript should be held to higher standards, avoiding imprecise and confusing ideas.

This work exhibits a notable lack of knowledge of the literature related to the “delayed choice” or the “quantum eraser”; the procedure of placing polarizers in front of the detectors, in addition to determining a projective measurement, is fulfilling a “quantum eraser” type role.

Among the most notable omissions is the recent proposal by Ionicioiu & Terno (Phys. Rev. Lett. 107, 230406 (2011)) to place the second beam splitter (BS2) in a present/absent state, in other words, in an open/closed quantum superposition state of the MZI, which produces behaviors that “mixed” the particle-like/wave-like character. This proposal, termed “Wheeler delayed choice quantum experiment”, has already been verified in numerous experiments, for instance, Nat. Photonics 6, 600 (2012); Physics. Rev. A 85, 032121 (2012); Sci Rep 13, 9758 (2023), among others. Something similar can be said about the Quantum Eraser literature, which is practically not mentioned in the text, except in reference 4. In conclusion, this area presents a profuse and abundant bibliography that the authors should review more carefully.

A final omission that should be discussed is the lack of (or difficulty in) the experimental implementation of the proposal. According to current standards of quantum optics laboratories, this does not seem to be difficult to implement. For example, in Science 338, 637 (2012), the authors use an entangled photon source where the particle/wave-like behavior of a single photon in an MZI is determined with the help of the second entangled photon in a HBT (PBS).

Minor comments

Phase $\phi$ used in equation 2 appears in figure 2, which is confusing because this phase comes from state preparation and not from a phase shifter as fig. 2 suggests.
Please maintain order in tensor products. By definition of the tensor product, a strict order in the modes should be maintained. The text, in a sloppy way, constantly changes order; e.g., equations (3), (4), (6), etc.
Entropic analysis of the wave-particle duality is interesting. However, the results presented in the MS are a little bit naive. There are strong relationships between entropic quantities and this kind of experimental context [e.g., Nat Commun 5, 5814 (2014)].

Final Recommendation

While the effort to discuss a new type of delayed choice experiment is important and interesting, the authors need to review, clarify, and address the comments made before the manuscript is suitable for publication.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

My comments are summarized in the attached file. 

Comments for author File: Comments.pdf

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This work revisits the wave-particle duality of photons, a foundational concept in quantum mechanics. It particularly addresses Wheeler’s Delayed-Choice Gedanken Experiment (WDCGE), where the decision to observe wave-like or particle-like behavior is made after the photon has entered the interferometer. The authors argue that using polarization-entangled photon pairs offers a resolution to the apparent paradox: photons behave as waves within the interferometer, independent of the presence of the second beam splitter. Their conclusion is supported by an analysis of Shannon entropy from photon counting data. The key insight is that the superposition principle remains the only true quantum mystery — photons don't change their nature retroactively but persist in a wave state unless disturbed by direct interaction.

 

• How are entangled photon pairs generated and used in the delayed-choice experiment?

• What role does polarization entanglement play in resolving the wave-particle paradox?

• How does the experiment rule out retroactive behavior, and what are its implications for interpretations like Copenhagen or many-worlds?

• How is Shannon entropy used in photon counting, and could other forms (e.g., von Neumann) reveal more?

• Are there limitations to the setup, can it extend to multi-particle systems, and what does it say about causality, time, and superposition?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The revised paper and the authors' reply address all my concerns.
On the updated paper, I recommend the publication.

An additional comment on typo: 
In 175th line, page 7, the "proyection" may be a typo. 

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript is in a suitable form for acceptance...