Dear Editor, this is a transfer of a manuscript to PRA which was originally submitted to PRL as manuscript number LD15929. As the Referees provided a rather detailed critique, we would like to address the points raised by them, and express our gratitude for their careful evaluation. Apart from addressing specific concerns of the Referees (see below), and a partial re-write following the particularly constructive comments of Referee B, we integrated the supplementary material into the main article as an Appendix to honor the style in PRA. We feel that the work presented in the manuscript is indeed introducing a new concept, together with experimental data, that it could match the scope of Physical Review A, and look forward for your consideration of the revised manuscript. With best Regards on behalf of all authors, Christian Kurtsiefer Our specific responses to Referee comments: ---------------------------------------------------------------------- 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. Reply: We thank the referee for reading the manuscript and correctly highlight how the visibility of the state is a relevant parameter to observe a violation of Bell's inequalities for collective measurements. In my opinion, the manuscript certainly does not deserves a publication in Physical Review Letters. The reported visibility requirements are ridiculously high. Reply: We do not agree on the statement that "The reported visibility requirements are ridiculously high": the minimal required visibility for three pairs is just ~85%. In section II.B and II.C we show that the largest cluster size can be evaluated for experimental visibilities reported in the literature. We furthermore support the statement by presenting an experiment, with its limited visibility, and show a violation for collective measurements. 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. Reply: We agree that a valid Bell-like experiment needs to be conducted in order to observe a violation of a Bell inequality, but there is no need to distinguish the individual pairs of measurements. The calculations are performed on local outcomes, not on correlated pairs. Moreover, I find the title misleading, as violation of a Bell inequality DOES NOT mean nonlocality of quantum mechanics. Reply: We are not claiming "the nonlocality of quantum mechanics", which we agree would be wrong: quantum theory is local, and indeed we never use the expression "quantum nonlocality". We are using "nonlocality" as a frequently-used shorthand for whatever is proved by the violation of Bell inequalities. This shorthand appears in the PACS list: though one may debate about its optimality, its use is at least legitimate. ---------------------------------------------------------------------- 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. Reply: We thank the Referee for the suggestion. We have modified the end of section II.A to clarify the concept. - 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? Reply: see previous point - 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. Reply: We have added a new figure showing the relationship between Vc and nc for both binning strategies. - 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). Reply: We have added such a figure in the appendix. 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… Reply: Indeed, this is the usual process of any Bell experiment: only one set of measurement is evaluated during each experimental round. The measurement rounds are then repeated several times with different choices of measurement settings in order to estimate all statistics appearing in the Bell inequality. Here, n particles are created and measured in each round of the protocol. We believe that the new figure 1 clarifies this point. - “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. Reply: We corrected the sentence as suggested by the Referee. - “2^n outputs” -> do the authors mean, 2^{2n} outputs? Aren’t there 2n photons being measured? Reply: In a Bell-type scenario, outputs are counted independently for each party (if Alice were to hold a qubit and Bob a qutrit, it could be that the number of outcome of Alice's measurement would not be equal to that of Bob's measurements). In our case, there are indeed just n photons on each side, an therefore 2^n possible outcomes for each party. The authors could consider a figure here to diagramize the protocol/scenario. Reply: We added a figure 1 to illustrate the overall protocol of a many-pair Bell experiment. C - when beta is introduced, it would be helpful to clarify that for optimal results, beta is a function of both n and V. Reply: We rewrote the entire section II.C. we think the rewrite is now clearer. - 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. Reply: See previous point. - for the analysis leading to equation (11), what value of beta is used here? Reply: See previous point. - in the SM equation (1), again, -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! Reply: We expanded the explanation of the numerical procedure, and introduce the parameter \beta for the majority vote case. -E - why is equation (7) numerical, instead of solvable directly? Reply: We clarified the origin of equation (7) as an analytical approximation of result obtained numerically. F - the experimental section is really excellently written. A couple details about the detectors might help, such as efficiency and noise (dark count / afterpulse)? Reply: We have added the efficiency and dark count rates for the APS detectors in the experimental section Minor points (probably language) - 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. Reply: We adopted the suggestion of the Referee. - IIB “… decreases roughly as ~1/sqrt(n) when n is growing.” -> what does n is growing means? Reply: We removed "when n is growing". - IIC, 2nd last paragraph: “… produces a violation with at least n = 14 pairs”. -> do the authors mean “at most n = 14 pairs”? Reply: Yes, the correct sentence is "[...] at most [...]" - SM: “we then estimate the sensibility” -> “sensitivity” Reply: We corrected the typo.