A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

Bierhorst, Peter

doi:10.1007/s10701-014-9811-3

Cited by 10 publications

(28 citation statements)

References 23 publications

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“…We introduce the following sequences of random variables. The notation and arguments borrow from earlier work 26 33 34 35 . Let the outputs of the boxes where i is used to label the i -th element, the histories of attempts previous to the i -th attempt, denotes the scores at each attempt and is the sequence of event-ready signals in the case of an event-ready experiment.…”

Section: Resultsmentioning

confidence: 99%

Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

Hensen

Kalb

Blok

et al. 2016

Sci Rep

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The recently reported violation of a Bell inequality using entangled electronic spins in diamonds (Hensen et al., Nature 526, 682–686) provided the first loophole-free evidence against local-realist theories of nature. Here we report on data from a second Bell experiment using the same experimental setup with minor modifications. We find a violation of the CHSH-Bell inequality of 2.35 ± 0.18, in agreement with the first run, yielding an overall value of S = 2.38 ± 0.14. We calculate the resulting P-values of the second experiment and of the combined Bell tests. We provide an additional analysis of the distribution of settings choices recorded during the two tests, finding that the observed distributions are consistent with uniform settings for both tests. Finally, we analytically study the effect of particular models of random number generator (RNG) imperfection on our hypothesis test. We find that the winning probability per trial in the CHSH game can be bounded knowing only the mean of the RNG bias. This implies that our experimental result is robust for any model underlying the estimated average RNG bias, for random bits produced up to 690 ns too early by the random number generator.

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Section: Resultsmentioning

confidence: 99%

Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

Hensen

Kalb

Blok

et al. 2016

Sci Rep

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“…assumption. : allowing for memory does not increase the probability of violating the CHSH inequality under the null hypothesis of local realism [19].…”

Section: Relevance Of the Gaussian Approximationmentioning

confidence: 91%

Test of the no‐signaling principle in the Hensen loophole‐free CHSH experiment

Adenier

Khrennikov

2017

Fortschritte der Physik

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We analyze the data from the loophole-free CHSH experiment performed by Hensen et al, and show that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger.

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“…Hence, in the case of a Bell experiment, a small P value can be regarded as strong evidence against the hypothesis that the experiment was governed by an arbitrary LHVM. There is extensive literature regarding the methods for evaluating the P value in Bell experiments [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and discussions regarding the analysis of concrete experiments and loopholes. [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] Previous approaches to obtain such P values known from the literature can be roughly divided into two categories.…”

Section: Introductionmentioning

confidence: 99%

(Nearly) optimal P values for all Bell inequalities

Elkouss

Wehner

2016

npj Quantum Inf

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A key objective in conducting a Bell test is to quantify the statistical evidence against a local-hidden variable model (LHVM) given that we can collect only a finite number of trials in any experiment. The notion of statistical evidence is thereby formulated in the framework of hypothesis testing, where the null hypothesis is that the experiment can be described by an LHVM. The statistical confidence with which the null hypothesis of an LHVM is rejected is quantified by the so-called P value, where a smaller P value implies higher confidence. Establishing good statistical evidence is especially challenging if the number of trials is small, or the Bell violation very low. Here, we derive the optimal P value for a large class of Bell inequalities. What is more, we obtain very sharp upper bounds on the P value for all Bell inequalities. These values are easily computed from the experimental data, and are valid even if we allow arbitrary memory in the devices. Our analysis is able to deal with imperfect random number generators, and event-ready schemes, even if such a scheme can create different kinds of entangled states. Finally, we review requirements for sound data collection, and a method for combining P values of independent experiments. The methods discussed here are not specific to Bell inequalities. For instance, they can also be applied to the study of certified randomness or to tests of noncontextuality.

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A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

Cited by 10 publications

References 23 publications

Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

Loophole-free Bell test using electron spins in diamond: second experiment and additional analysis

Test of the no‐signaling principle in the Hensen loophole‐free CHSH experiment

(Nearly) optimal P values for all Bell inequalities

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