Introduction to Bell’s Inequality in Quantum Mechanics†
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper describes itself as a pedagogical introduction to Bell's Theorem. As such, it contains no original research and the editor should consider whether it is still suitable for publication in the journal.
Judged by its own terms, the paper consists of an extensive review of the subject, rather than an introduction, and it does not make clear what level of readership it is aimed at. It is unlikely that any undergraduate degree course would contain material beyond section 3 of the paper.
I have identified several detailed points that the authors should consider.
Around (44), the term "supremum" is used. This is a technical term used in set theory, which does not apply in the present context. I suggest that it is replaced by "maximum".
At several points including (54), (87), (104), (136) a strange unusual symbol is used. This should be clarified.
The expression on the RHS of (111) is said to be close to 2\sqrt(2) when \eta and \sigma are small. This is true only when these quantities are equal as well as small. This is assumed in the later example, but should be spelled out from the start.
The authors should carefully recheck the text for possible further errors
Author Response
Please, see attachment
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsIntroduction to Bell’s Inequality in Quantum Mechanics by Sorella et al
This paper gives a pedagogical introduction to Bell’s theorem aimed at postgraduate students or physicists who are not familiar with the topic but wish to learn about it.
After introducing the physical basis and mathematical concepts needed for a discussion of the topic, the authors procced with their exposition.
The first batch of topics discussed include the CHCH inequality, Tsirelson’s bound and Gisin’s theorem. The second topic is the CHSH violation for spin 1 and spin 3/2 states. The third topic is Bell’s violations for entangled coherent and squeezed states. Finally come the Mermin inequalities for the GHZ states.
The authors’ discussion of all the topics seems to be correct and free of errors, as far as I can judge. I have not carefully checked all the many formulae and results given, and will leave it to the authors to proofread their work and make sure that no errors have crept in.
When it comes to a review like this, the choice of which topics to include and how to discuss each of them is a matter on which I suspect there will be a wide range of opinions. I have my often preferences, which do not always agree with those of the authors. For example, I would discuss CHSH and Gisin’s theorem rather differently. But I see nothing wrong with the approach the authors have used.
The subject of coherent and squeezed states discussed by the authors has been covered extensively in the text by Gerry and Knight, which has recently come out in a second edition. This may be of use to students interested in this topic and I suggest the authors add it to their references. It is -- Introductory Quantum Optics 2nd Edition, by Christopher C. Gerry and Peter L. Knight, Cambridge University Press, 2024.
The authors could make the work more useful to their intended audience by publishing the answers and/or hints to the various problems in an appendix.
Comments on the Quality of English Language
English is OK
Author Response
Please, see the attachment
As suggested, the ref. by Gerry and Knight has been added, see ref.[30]
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsMy comments regarding the publication of this paper are pointed out below:
1. The underlying physical concept studied in this paper is very good, and the authors have managed to present it in a very elaborative fashion.
2. The results derived in this paper are original and correct.
3. Only I found that the reference list is not complete.
Based on the above mentioned points, I recommend a minor revision of the present version of the draft.
Author Response
Please, see attachment
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have addressed all the points I raised.
