Pearle’s Hidden-Variable Model Revisited
Round 1
Reviewer 1 Report
This manuscript reconsiders an old model with hidden variables. While models with hidden variables are usually considered excluded by Bell's theorem, there is a possible ``detection loophole'': models where one assumes that not all particles are detected. One such model is reconsidered here, correcting some mistakes and more importantly simulating it with the piece of software ``R''. I found the paper interesting and well written, and I suggest it for publication.
Author Response
Thank you for your appreciation of the paper.
Reviewer 2 Report
The manuscript explores Pearle's local hidden variables model which accurately reproduces quantum singlet-state correlations of quantum theory by exploiting data-rejection as a possibility. The central result of the paper is the discovery of a problematic renormalization method, with possibly important implications for quantum modeling of behavior of entangled states. I support its publication without further change. However, I would ask the author to make an additional effort to seek out other, related papers so that the impact of this paper for future research can be increased.
Author Response
Dear referee, you ask me to "make an additional effort to seek out other, related papers so that the impact of this paper for future research can be increased." I am happy to do so; and I will do this as soon as possible. The list of related papers could be extremely long; and of course, would also require some discussion. I would certainly appreciate receiving any suggestions from you, which I suppose you can do anonymously via the journal editors. Thanks in advance, if you are able to give some help in this way! No comments are needed, just a list of references, if you have any to hand.
There already exist some recent survey papers on loopholes in Bell-type experiments which will be useful, I will start with reading some of them. And very recently I was reading a very old paper by A. Shimony which referred to work on detection-loophole models from the early days, which I had never heard of.
Reviewer 3 Report
This manuscript reports some numerical results on the hidden-variable theory published by Pearle in 1970. I am not familiar with the model, as it seems from this manuscript as well that it predicts some features of singlet correlation measurements that are not physical. The manuscript looks more like a student report than a scientific paper, with snippets of code and unpolished figures. The manuscript has no connection to entropy, and I think it would be more suitable (with polishing) to a pedagogical journal such as American Journal of Physics.
I do not think this manuscript is appropriate for Entropy.
Author Response
Dear referee, thanks for your comments, even if they were not very positive. You wrote that you are not familiar with the model, "as it seems from this manuscript as well that it predicts some features of singlet correlation measurements that are not physical". This is absolutely true, and was already mentioned by Pearle himself. There are alternative models which do not have this defect, as I mention in my paper.
My paper is about simulation models which reproduce the singlet correlations. I therefore don't think that snippets of code are out of place, though obviously, not everyone likes to (or needs to) study code. You say that the figures are "unpolished". I can certainly make them more professional, though my aim was to show what one can get quickly and easily by simple and transparent code. My aim was to show that the Pearle model is in fact easy to implement in real simulation experiments. I will see if some improvements to the figures can be easily implemented.
Indeed the paper's original scientific contributions are modest; it could be characterised as a pedagogical work. Still, for many years Pearle's paper was thought of as having made purely a theoretical contribution to the literature on the detection loophole - thus it established a bound to detection efficiency, which would need to be exceeded before a "loophole free" experiment was possible. Though actually this interpretation was also wrong, since if one chooses different states and different measurements, less efficient detectors are needed! It also seems that nobody had checked the maths, either (of course, if you find the model uninteresting because of its unphysical features, then you won't bother to verify the formulas).
It seems that nobody at all noticed that Pearle's model was very closely related to models which had been invented by a host of Bell critics, which almost but not exactly reproduced the singlet correlations. This is especially the case since many of the formulas in the paper are wrong.
I am glad that you do agree that the paper should get published somewhere.
Indeed there is no real connection with the concept of entropy. Yet there are many papers in the journal Entropy on quantum information, Bell's theorem, and Bell-type experiments (and many editors who work in these fields).
