Destructive Interference as a Path to Resolving the Quantum Measurement Problem

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript by James Camparo presents an articale fousing on the Quantum Measurement Problem from the Destructive Interference. The author provided a very good method and thinking to elucidate how to solve the problem. The theoretical methods and his theoretical analysis are reliable and looks excellent. So think this is a good work and should be proper for publication in the present form.  I have no question or special comments for it.    

Author Response

The Reviewer had "no questions or special comments."  We appreciate the time the Reviewer took to examine our work.

Reviewer 2 Report

Comments and Suggestions for Authors

See attached PDF.

Comments for author File: Comments.pdf

Author Response

The Reviewer saw no major problem with our work and recommended that it be published as is.  We want to thank the Reviewer for the time that they took to examine our paper.

Reviewer 3 Report

Comments and Suggestions for Authors

General Evaluation

The manuscript provides a novel perspective on the quantum measurement problem by introducing disjoint eigenphase sets and proposing a phase-locking mechanism between the quantum system and a classical measuring device. This approach frames wavefunction collapse as a natural consequence of interference, rather than as an ad hoc postulate. The work is original, clearly presented, and relevant both to foundational debates and to practical aspects of quantum technologies.

Strengths

1. Originality: The proposed phase-based approach is innovative and distinct from traditional interpretations such as Copenhagen, Many Worlds, Decoherence, and Spontaneous Collapse models.

2. Conceptual consistency: The framework avoids hidden-variable interpretations and remains consistent with Bell inequalities, the uncertainty principle, and the linearity of quantum mechanics.

3. Clarity of exposition: The article is well structured, progressing from a review of existing solutions to a careful development of the author’s proposal.

4. Relevance: The discussion aligns with the rapidly developing field of quantum sensing and offers conceptual tools that may influence future experimental designs.

Minor Suggestions

• Some stylistic polishing of the introduction would improve the narrative flow.

• It would be beneficial to expand the discussion on possible experimental tests of the proposed phase-locking mechanism, even speculatively.

• The manuscript could also acknowledge the role of excitation-pathway interference in quantum systems. Such interference phenomena — central to atomic and molecular spectroscopy, quantum optics, and multi-path interferometry — highlight how phase coherence and indistinguishability of excitation routes directly shape measurement outcomes. Discussing this connection would strengthen the physical intuition behind the proposal and emphasize its experimental relevance.

• I recommend adding the following references to enrich the theoretical and applied context of quantum measurements:

  •  
  • Y. Aharonov and L. Vaidman, “The Two-State Vector Formalism of Quantum Mechanics,” in Time in Quantum Mechanics, Lecture Notes in Physics, vol. 734, pp. 399–447 (Springer, 2009). 

  • [ New Journal of Physics, v. 17, n. 9, p. 093010, (2015)].

  • H.M. Wiseman and G.J. Milburn, Quantum Measurement and Control, Cambridge University Press (2010).

  • [Acta Physica Slovaca 69, 1–74 (2019)].

These references and the inclusion of excitation-pathway interference would further connect the conceptual framework of the manuscript to concrete physical phenomena.

Recommendation

The manuscript is an important and creative contribution to the literature on quantum measurement. With minor textual revisions, the addition of relevant references, and a brief mention of excitation-pathway interference, it will be ready for publication in Quantum Reports.

Final Recommendation: Accept with minor revisions.

Author Response

1. The Reviewer suggested that “some stylistic polishing of the introduction would improve the narrative flow.”  We have done some rewording of the introduction to hopefully make it clearer.

2. The Reviewer suggested that “it would be beneficial to expand the discussion on possible experimental tests of the proposed phase-locking mechanisms, even speculatively.”  We now state at the end of Appendix C

The fact that this particular process for phase locking relies on a “number asymmetry”: one quantum measurand interacting with an Avogadro’s number of measuring-device quantum entities, suggests an experimental means of studying the process (at least conceptually). One could imagine building up a macroscopic measuring device one quantum-entity at a time, and as the number of quantum-measurement entities grows examine the measuring device’s ability to force wavefunction collapse. Perhaps this could be accomplished with trapped ions as the measuring device since it is possible to form trapped-ion crystals in a linear ion trap [51]. If the rotary collective motion of the ion-crystal could be used as the measurement response for a linearly polarized electromagnetic field [52], it might be possible through that collective motion to watch wavefunction collapse occur (actually photon state-vector collapse) as the number of ions in the crystal grew from one or two to many tens and then thousands. Obviously, to conduct such an experiment would require excellent sensitivity to the ions’ collective motion and would necessitate the use of single photons. Thus, one can imagine that the signal-to-noise ratio in such an experiment would be a nightmare, and that there would be many additional daunting experimental challenges. However, the fact that one can imagine such an experiment to test a possible resolution of the measurement problem is fascinating, and if accomplished would be extremely illuminating of quantum mechanics’s subtle structure.

3. The Reviewer suggested that the manuscript “acknowledge the role of excitation-pathway interference,” as this would “highlight how phase coherence and indistinguishability of excitation routes directly shapes measurement outcomes.  We now state in Section 2.6 (lines 235 – 240)

An excellent experimental/technological example of this is provided by atomic clocks based on Coherent Population Trapping (CPT) [37]. With CPT two routes of optical excitation within an atom are simultaneously excited. However, since the two routes (i.e., matrix elements) have different phases, they destructively interfere, which results in no optical absorption though both optical excitation routes are resonantly excited.

4. The Reviewer suggested that I add several references. I felt that two of the references would take the discussion of the manuscript too far afield.  Consequently, I did not add those references.  However, two of the Reviewer’s other recommendations were ones that I was unaware of and were very relevant to the manuscript’s topic.  The two references that I added are: “Quantum Measurement and Control,” which now appears as Ref. 48, and “An introduction to quantum measurements with a historical motivation,” which now appears as Ref. 19.

Reviewer 4 Report

Comments and Suggestions for Authors

James Camparo's work focuses on measurement theory in quantum mechanics and seeks to develop a method to justify a form of wave function collapse through the use of random phases. I believe that this highly forward-looking work deserves publication, but I have two important points to mention that the author should take into account when revising his work:
1)   Invoking the phases of wave functions to explain collapse   is not new, and David Bohm, in particular, in his work described in ref. 39, already describes this type of idea (which in a way anticipates the theory of decoherence). This needs to be clarified and commented on.  Another relevant work is probably that of Kofler and Brukner [Phys. Rev. Lett. 99, 180403], which also seeks to justify the measurement theory rather than alternative approaches to decoherence. 
2) I mention that the assertion that hidden variable theories have been refuted by Bell's theorem is false: only local variables are excluded, and theories such as those of de Broglie Bohm survive.

 

Author Response

1. The Reviewer suggested that we include David Bohm’s use of phase in the measurement problem, which is described in his textbook on quantum mechanics, as well as the article by Kofler & Brukner, “Classical world arising out of quantum physics under the restriction of coarse-grained measurements.  Examining the paper by Kofler & Brukner, I felt that inclusion of their work would take the discussion in the manuscript too far afield. Consequently, I did not include this reference.  However, the Reviewer’s suggestion to include some discussion of Bohm’s work was very appropriate. As a consequence, I now write in the Introduction (lines 75 – 86)

In this paper we want to revisit a solution pathway to the measurement problem first touched on by Bohm [20] and then more carefully pointed out by Pearle [21]. Bohm noted that every measurement involves an interaction, and that through the interaction the combined quantum-entity/measuring-device wavefunction develops a random phase. On average this random phase keeps measuring-device “pointer states” solely associated with their corresponding quantum-particle eigenstates. Unfortunately, in Bohm’s analysis these random phases do nothing to resolve the problem of wavefunction collapse. Pearle took the phase idea a bit further, arguing that if the phase of a wavefunction were a random variable, then along with a nonlinear Schrödinger equation this random phase would lead to wavefunction collapse. Here, we also focus on wavefunction phase as central to the measurement problem. However, different from Pearle we take quantum mechanics as linear.

2. The Reviewer also pointed out (quite rightly) that our discussion of Hidden Variable Theory was really an examination of Local Hidden Variable Theories. This has been corrected throughout the manuscript.