---------------------------------------------------------------------- Report of Referee A -- LD15929/Poh ---------------------------------------------------------------------- Manuscript "Experimental many-pairs nonlocality" present a Clauser-Horne-Shimony-Holt experiment withan assumption that systems are treated collectively, rather than individually. Consequently, for the derivation of the CHSH inequality to hold, one needs to propose a function of all gathered results to interval <-1,1>. Two such maps are proposed, the majority voting and and parity binning. In my opinion, the manuscript certainly does not deserves a publication in Physical Review Letters. The reported visibility requirements are ridiculously high. Additionally applying the functions anyhow requires a valid Bell experiment to be conducted since we need to perform calculations on products of local outcomes, so individual pairs of measurements need to be distinguished. In total, I don't see how this result brings any new essential knowledge. Moreover, I find the title misleading, as violation of a Bell inequality DOES NOT mean nonlocality of quantum mechanics. ---------------------------------------------------------------------- Report of Referee B -- LD15929/Poh ---------------------------------------------------------------------- I found the work reported in “Experimental many-pairs nonlocality” by Poh et al., to be an interesting approach to Bell Inequalities. The purpose of the article is to examine the scenario when two parties (Alice & Bob) try to violate a Bell Inequality, but cannot record results from each individual particle they measure. Instead A&B can only measure/record some aggregate statistic on an ensemble of individual particles. Specifically, the authors examine a “majority vote” scheme, where A&B can only measure/record the most popular outcome of a binary-output measurement, and a “parity” scheme, where A&B can only measure/record the parity of the output. The former scheme was introduced in 2008, the latter scheme is new and introduced in this manuscript. The manuscript is well written, the analysis seems very well done, and the experimental work appears excellent. However, I’m not convinced that it’s sufficiently interesting for Phys Rev Lett, given that 1- the first scheme nearly 10 years old, and 2- the advantage of the second/new scheme seems marginal over the first: specifically, the partity scheme gives higher bell inequality violations, and violations that decrease slower with increasing ensemble size, but both only when the visibility is already very high. In fact, the visibility must be higher than what the authors have achieved in their "high-visibility source". I would definitely support publication in PRA, but would ask the authors to consider the following points. A - It seems that there are two important figures of merit for these schemes. 1- the value of the Bell inequality (especially when > 2), and 2- the critical pair number n_c and critical visibility V (both of which are functions of the other, for fixed values) These values are discussed throughout the article, but a more focused approach/section that clearly states or presents these quantities could be helpful. X- end of section IIa: “we estimate a lower bound on the Werner state visibility V… at which a violation is observed” -> could this be defined as critical visibility? X- For both sections IIB, IIC, what could be useful is a plot of critical V vrs. critical n, showing a curve where everything below the curve wouldn’t violate a bell inequality. The Vc-nc curves for the two schemes could be presented on the same graph so as to compare the majority vote scheme to the parity scheme. - Furthermore, such a plot could be turned into a color plot, or 3D plot, showing the S parameter value (when > 2) for each V-n point… This might work better in the Supplemental Material though (and in fact, would be more general plots than the cases presented in the SM). B - I found the description of the scenario in IIa 1st & 2nd paragraph a bit confusing: - “Each party submits all its n particles to the same single-particle measurement” -> so n particles are used for a single measurement… which means we must repeat this procedure several times with different settings to get the 4 correlation coefficients for the Bell inequality. At this point in the manuscript, it’s not clear where protocol repetition occurs… X- “each party performs two measurements” -> do the authors mean, one of two measurements? As all n particles are submitted to the same single-particle measurement. - “2^n outputs” -> do the authors mean, 2^{2n} outputs? Aren’t there 2n photons being measured? The authors could consider a figure here to diagramize the protocol/scenario. C - when beta is introduced, it would be helpful to clarify that for optimal results, beta is a function of both n and V. - is the beta_0 chosen just below equation (10) optimal? [ beta = sqrt(ln(3))/2/sqrt(n) ]It’s not clear from the text why this value is used. - for the analysis leading to equation (11), what value of beta is used here? - in the SM equation (1), again, X-D - The parameter Beta (which determines measurement settings) is discussed extensively for the parity scheme. Can a beta be introduced into the analysis of the Majority Vote scheme? Or is there a good reason why this wouldn’t help? It seems odd that for most of the manuscript Beta is discussed solely with relation to the parity scheme… until section IIIB, figure 2., where suddenly Beta is a parameter for the majority vote scheme! X-E - why is equation (7) numerical, instead of solvable directly? F - the experimental section is really excellently written. A couple details about the detectors might help, such as efficiency and noise (dark count / afterpulse)? Minor points (probably language) X- 3rd paragraph: “maximal cluster size n_c” is used, but I think this is the same concept as “critical pair number”. For easy-of-reading, I would be helpful to stick to one description of this concept throughout the article. X- IIB “… decreases roughly as ~1/sqrt(n) when n is growing.” -> what does n is growing means? X- IIC, 2nd last paragraph: “… produces a violation with at least n = 14 pairs”. -> do the authors mean “at most n = 14 pairs”? X- SM: “we then estimate the sensibility” -> “sensitivity”