2011
DOI: 10.1103/physreva.84.062118
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Asymptotically optimal data analysis for rejecting local realism

Abstract: Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p-value. We propose a prediction-based-ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantu… Show more

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Cited by 70 publications
(167 citation statements)
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“…Corrections due to finite samples, and extension to non-i.i.d. scenarios can in principle be done with the techniques in [28,44,45].…”
Section: Assumptions Of This Papermentioning
confidence: 99%
“…Corrections due to finite samples, and extension to non-i.i.d. scenarios can in principle be done with the techniques in [28,44,45].…”
Section: Assumptions Of This Papermentioning
confidence: 99%
“…It is useful to stress that, as written, (2) contains an additional assumption, namely that λ itself is chosen independently in each run according to the distribution p(λ). Under measurement independence, it can be proved that this is ultimately not a restriction for Bell tests, although one has to be careful in interpreting statistics from finite samples [15][16][17]. Measurement independence cannot be denied in a systematic way without undermining the scientific method itself (if a clinical trial is to make sense, whether each patient receives the drug or the placebo cannot depend on the any details of the patients' conditions).…”
Section: Measurement Dependence and Its Basic Consequences A Meamentioning
confidence: 99%
“…Let P (ab|xy) be an arbitrary no-signaling distribution with x ∈ {1, ..., m A } and y ∈ {1, ..., m B }. For any pair of settings (x,ȳ), there exists a local distribution P L (ab|xy) such that P L (ab|xy) = P (ab|xy) (17) for…”
Section: A Reaching the No-signaling Limitmentioning
confidence: 99%
“…Observation of a negative value for W then leads to the conclusion that the measured system is Bell correlated. However, reaching such a conclusion in the presence of finite statistics requires special care [14,15]. In particular, an assessment of the probability with which a non-Bell-correlated state could be responsible for the observed data is required before concluding about the presence of Bell correlations without further assumptions.…”
mentioning
confidence: 99%
“…Note that such a conclusion does not follow straightforwardly from the violation of the witness by a fixed number of standard deviations. Indeed, standard deviations inform on the precision of a violation, but fail at excluding arbitrary local models [15], including, e.g., models which may show non-Gaussian statistics with rare events. We thus look here for a number of experimental runs which is sufficient to guarantee a p value lower than a given threshold for the null hypothesis "The measured state is not Bell correlated."…”
mentioning
confidence: 99%