Experimental Proof That Bell’s Inequality Cannot Falsify Local Realism, Together with Corresponding Cause Analysis and Conjectures

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

I have three major concerns about this manuscript.

1. In Experiment 3 (Eqs. In sections 7–12, the authors apply Malus’s law and Pearson correlation to reproduce a cosine-type correlation, claiming a violation of Bell’s inequality. However, the result is not a valid Bell test. 
2. The claim that “independent photons with orthogonal polarization violate Bell inequality” is highly questionable. 
3. The derivation of the CHSH inequality (Eqs. 1–6) already assumes very general conditions and is not restricted in the way the authors claim. The statement that Bell inequality applies only to “binary events” and fails for continuous variables is not correct. Continuous-variable quantum systems can be also treated within Bell-type frameworks using appropriate mappings. 

Author Response

Comments 1: In Experiment 3 (Eqs. In sections 7–12, the authors apply Malus’s law and Pearson correlation to reproduce a cosine-type correlation, claiming a violation of Bell’s inequality. However, the result is not a valid Bell test. 

Response 1: [You are absolutely right. Experiment 3 in our manuscript, which tests Bell inequalities using independent light beams, is indeed not a test of conventional Bell inequalities. Nevertheless, the main purpose of this experiment is to demonstrate that conclusions consistent with both experimental observations and quantum mechanical predictions can also be obtained within classical optics and statistical theory, thereby providing an experimental foundation for analyzing the violation of Bell inequalities by independent photons with orthogonal polarizations observed in Experiment 2.]

 

Comments 2: The claim that “independent photons with orthogonal polarization violate Bell inequality” is highly questionable. 

Response 2: [The core logic of the manuscript on this point is as follows: independently prepared photons with orthogonal polarizations naturally possess local realism, yet experiments show that they still violate Bell inequalities. It is therefore inferred that there is no necessary connection between the violation of Bell inequalities and local realism.

We believe this logic is rigorously valid. Should you have any concerns or objections, we would be grateful if you could kindly point them out to us.]

 

Comments 3: The derivation of the CHSH inequality (Eqs. 1–6) already assumes very general conditions and is not restricted in the way the authors claim. The statement that Bell inequality applies only to “binary events” and fails for continuous variables is not correct. Continuous-variable quantum systems can be also treated within Bell-type frameworks using appropriate mappings. 

Response 3: [To the best of our knowledge, the authors have not identified any experiments demonstrating the violation of continuous-variable Bell inequalities. If such experiments exist, we would highly appreciate it if you could kindly point them out to us. We will carefully study the relevant literature and revise our manuscript accordingly. Thank you very much for your assistance.]

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The most part of present experiments testing nonlocality via the violation of the Bell’s inequality are indeed based on pairs of photons emitted in an entangled state by a common source. And now comes the question what if the Bell’s tests are performed using truly independent photons with inherent local realism? What outcomes are to be expected in this case? In reply to this issue, Ting Zhou in his work proposes a series of Bell-test experiments with independent photon pairs.  In result, the first experiment demonstrates that fully independent, uncorrelated photons satisfy Bell’s inequality. The second experiment involves the orthogonally polarized independent photons. In this case, the Bell’s inequality has been shown to be violated, despite the inherent local realism of the participating orthogonally polarized independent photons. And the third experiment showed that replacing single photons with monochromatic light beams yields transmittance correlations that also violate Bell’s inequality, quantitatively matching quantum-mechanical predictions for entangled photon pairs.

The author has explained the observed violation in optical beam experiments and proposed a unifying conjecture: single-photon transmission through a polarizer must be a continuous, non-binary process, eliminating the discrepancy between classical expectations and experimental Bell-test results.

          In general, the topic of this work is interesting for readers, as the issue of quantum entanglement and the violation of Bell’s inequality are much discussed lately. And, this work contributes much to the contemporary discussions, addressing a specific gap between classical expectations and experimental Bell-test results.

However, the presented work fails to discuss the other published material on the topic that undoubtedly should have been done in the first place in the Introductory section. It hardly can be said that such works are absent and there is nothing to write about. For instance, Yurke and Stoler have shown that Bell’s inequalities can be violated even if the two particles do not originate from a common source [B. Yurke and D. Stoler, Phys. Rev. Lett. 68, 1251 (1992); Phys. Rev. A 46, 2229 (1992)]. Pittman and Franson [Phys. Rev. Lett. 90, 240401 (2003)] described an experimental violation of Bell’s inequality using one photon from parametric down-conversion and a second photon from an attenuated laser beam. Quantum interference patterns with visibilities as high as 91% were obtained using the two photons from independent sources. Thus, they showed that nonclassical interference effects can be obtained using photons from independent sources, which is an important requirement for optical approaches to quantum information processing. Such works are many, and the author of the present manuscript should deign to discuss them as much as possible in the Introductory section and clearly delineate why his work is original and what does it add to the subject area.

Specific improvements that can be recommended for this manuscript are scarce, as the work represents a clearly-written text with logically consistent schematics of experiments. Although, a few recommendations/queries are in order.

1. If it is possible, the resolution of Figure 1 is better to be increased.
2. Please, be more specific about the local realism. One sentence in the beginning of manuscript is not enough.
3. For readers, it would be interesting to know what is the practical meaning of the obtained results. In particular, what do they entail for superconducting quantum computing?

In all other aspects, the manuscript is fine, including the conclusions which are consistent with the evidence and arguments presented in the study and the references which are appropriate and relevant.

          By the contents of this work and the way it is written, I have decided to recommend it for publication in Quantum Reports after minor revision.

 

Author Response

Comments 1: If it is possible, the resolution of Figure 1 is better to be increased.

Response 1: [Thank you for your comment. I will redraw this figure clearly in the revised manuscript.]

 

Comments 2: Please, be more specific about the local realism. One sentence in the beginning of manuscript is not enough.

Response 2: [Thank you for your suggestion. I will clarify the connotation of local realism in the revised manuscript.]

 

Comments 3: For readers, it would be interesting to know what is the practical meaning of the obtained results. In particular, what do they entail for superconducting quantum computing?

Response 3: [Thank you for your suggestion. Thank you for your suggestion. I will consider adding relevant content in a related future paper.]

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript proposes that Bell's inequality cannot falsify local realism by demonstrating violations using independent orthogonally polarized photons and macroscopic light beams. While thought-provoking, the manuscript requires significant revisions to address fundamental physics concepts, experimental validation, and literature context before being suitable for Quantum Reports. Please address the following comments:

1. The introduction lacks the rigorous mathematical definition of the specific Bell/CHSH inequality being tested. Please improve the introduction by explicitly defining the quantum mechanical correlation function E(θ₁, θ₂) and contrasting it early on with the classical "Karl Pearson's correlation" used later in the text.
2. Please expand the conclusion to include a rigorous comparative analysis between your proposed independent-photon violation and standard SPDC-generated entangled pairs. The outlook must address ongoing challenges: if quantum entanglement is merely an artifact of orthogonal polarizations as you conjecture, how can future experimental setups practically and definitively distinguish between genuine non-locality and your proposed local realism model while accounting for standard detection and locality loopholes?
3. The manuscript ultimately relies on a "thought experiment involving gradual attenuation of light intensity down to the single-photon regime" to support its core conjectures. To validate this hypothesis and elevate the quality of the paper, the author must actually perform this attenuation experiment using true heralded single-photon sources and coincidence counting. Relying solely on macroscopic continuous beams is insufficient to challenge Bell's theorem, which is fundamentally built on discrete quantum detection events.
4. The demonstration of Bell-like inequality violations using classical or independent light beams is heavily documented in the context of "classical entanglement" (e.g., structural non-separability of polarization and spatial modes). The author must extend the literature review to benchmark their macroscopic results against existing studies on classical Bell violations. This is necessary to clearly define the novelty of your specific approach and explain why your findings challenge local realism differently than known classical analogs.
5. The theoretical analysis asserting that Bell's inequality is strictly restricted to "binary events" requires major improvement. Continuous-variable Bell inequalities do exist in modern quantum mechanics. The author must rigorously address the mathematical and physical transition between continuous intensity correlations (Malus's law) and discrete binary photon detections. Conflating continuous macroscopic variables with discrete quantum states undermines the critique of local hidden variables.

Author Response

Comments 1: The introduction lacks the rigorous mathematical definition of the specific Bell/CHSH inequality being tested. Please improve the introduction by explicitly defining the quantum mechanical correlation function E(θ₁, θ₂) and contrasting it early on with the classical "Karl Pearson's correlation" used later in the text.

Response 1: [Thank you for your suggestion. I will add the correlation function calculated according to quantum mechanics in the introduction.]

 

Comments 2: Please expand the conclusion to include a rigorous comparative analysis between your proposed independent-photon violation and standard SPDC-generated entangled pairs. The outlook must address ongoing challenges: if quantum entanglement is merely an artifact of orthogonal polarizations as you conjecture, how can future experimental setups practically and definitively distinguish between genuine non-locality and your proposed local realism model while accounting for standard detection and locality loopholes?

Response 2: [This manuscript does not propose any new model for local realism.

We only conjecture that the reason entangled photon pairs violate Bell inequalities in traditional Bell-test experiments is not a violation of local realism, but simply that the two photons are in orthogonal polarization states.

As to how to verify whether this conjecture is correct or the quantum-mechanical interpretation of local realism violation holds true, Experiment 2 in this paper serves as the demonstration.]

 

Comments 3: The manuscript ultimately relies on a "thought experiment involving gradual attenuation of light intensity down to the single-photon regime" to support its core conjectures. To validate this hypothesis and elevate the quality of the paper, the author must actually perform this attenuation experiment using true heralded single-photon sources and coincidence counting. Relying solely on macroscopic continuous beams is insufficient to challenge Bell's theorem, which is fundamentally built on discrete quantum detection events.

Response 3: [Thank you for your comment. This thought experiment is indeed not yet supported by practical experiments, and this will be a direction for our future efforts.

Nevertheless, the refutation in this paper against the disproof of local realism via Bell inequalities is not based on this thought experiment, but on Experiment 2 in the text: a real experiment showing that fully independent photons with orthogonal polarization directions still violate Bell inequalities.]

 

Comments 4: The demonstration of Bell-like inequality violations using classical or independent light beams is heavily documented in the context of "classical entanglement" (e.g., structural non-separability of polarization and spatial modes). The author must extend the literature review to benchmark their macroscopic results against existing studies on classical Bell violations. This is necessary to clearly define the novelty of your specific approach and explain why your findings challenge local realism differently than known classical analogs.
Response 4: [There are indeed many papers demonstrating the violation of Bell inequalities using classical or independent beams. I will follow your suggestion to supplement relevant references and provide corresponding explanations. However, the most significant difference between this work and previous related discussions is that we start from classical optical theorems and statistical formulas, yet arrive at the same conclusions as quantum mechanics. This indicates that quantum mechanics is not the only theory capable of explaining these experimental phenomena.]

 

Comments 5: The theoretical analysis asserting that Bell's inequality is strictly restricted to "binary events" requires major improvement. Continuous-variable Bell inequalities do exist in modern quantum mechanics. The author must rigorously address the mathematical and physical transition between continuous intensity correlations (Malus's law) and discrete binary photon detections. Conflating continuous macroscopic variables with discrete quantum states undermines the critique of local hidden variables.
Response 5: [To the best of our knowledge, the authors have not identified any experiments demonstrating the violation of continuous-variable Bell inequalities. If such experiments exist, we would highly appreciate it if you could kindly point them out to us. We will carefully study the relevant literature and revise our manuscript accordingly. Thank you very much for your assistance.]

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The Authors have revised the Manucript.

Comments on the Quality of English Language

Well written.

Author Response

Comments ：The Authors have revised the Manuscript.

Response: [Thank you for reviewing our revised manuscript. We have revised the manuscript according to the comments and hope it meets your approval.]

Reviewer 3 Report

Comments and Suggestions for Authors

Authors have adequately addressed several of my key comments, particularly by committing to update the introduction with the necessary mathematical definitions and by expanding the literature review to benchmark against classical entanglement studies. While the lack of a true single-photon attenuation experiment remains a limitation, I understand it is scoped for future work and that Experiment 2 serves as the primary basis for your current argument. I am satisfied with these revisions and recommend the manuscript for acceptance.

Author Response

Comment: Authors have adequately addressed several of my key comments, particularly by committing to update the introduction with the necessary mathematical definitions and by expanding the literature review to benchmark against classical entanglement studies. While the lack of a true single-photon attenuation experiment remains a limitation, I understand it is scoped for future work and that Experiment 2 serves as the primary basis for your current argument. I am satisfied with these revisions and recommend the manuscript for acceptance.

Response: [We sincerely appreciate your careful review and positive comments on our revised manuscript. Thank you for recognizing our efforts in improving the introduction and literature review. We acknowledge the limitation concerning the single-photon attenuation experiment and have marked it as future work, and we are pleased that you accept Experiment 2 as the main evidence for our conclusions. We are very grateful for your recommendation for acceptance.]