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arXiv:1607.04177 · Physical Review A

Consequences of recent loophole-free experiments on a relaxation of measurement independence

Alejandro Andrés Hnilo

Published Feb 2, 2017• 7 citations
arXivHTMLPDF

Abstract

Recent experiments using innovative optical detectors and techniques have strongly increased the capacity of testing the violation of the Bell's inequalities in Nature. Most of them have used the Eberhard's inequality (EI) to close the ``detection'' loophole. Closing the ``locality'' loophole has been attempted by spacelike separated detections and fast changes of the bases of observation, driven by random number generators of new design. Also, pulsed pumping and time-resolved data recording to close the ``time-coincidence'' loophole, and sophisticated statistical methods to close the ``memory'' loophole, have been used. In this paper, the meaning of the EI is reviewed. A simple hidden variables theory based on a relaxation of the condition of ``measurement independence,'' which was devised long ago for the Clauser-Horne-Shimony and Holt inequality, is adapted to the EI case. It is used here to evaluate the significance of the results of the recent experiments, which are briefly described. A table summarizes the main results.

DOI
10.1103/physreva.95.022102

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Recent experiments using innovative optical detectors and techniques have strongly increased the capacity of testing the violation of the Bell's inequalities in Nature. Most of them have used the Eberhard's inequality (EI) to close the detection'' loophole. Closing the locality'' loophole has been attempted by spacelike separated detections and fast changes of the bases of observation, driven by random number generators of new design. Also, pulsed pumping and time-resolved data recording to close the time-coincidence'' loophole, and sophisticated statistical methods to close the memory'' loophole, have been used. In this paper, the meaning of the EI is reviewed. A simple hidden variables theory based on a relaxation of the condition of ``measurement independence,'' which was devised long ago for the Clauser-Horne-Shimony and Holt inequality, is adapted to the EI case. It is used here to evaluate the significance of the results of the recent experiments, which are briefly described. A table summarizes the main results.
In a local realist model, physical properties are defined prior to and independent of measurement and no physical influence can propagate faster than the speed of light. Proper experimental violation of a Bell inequality would show that the world cannot be described with such a model. Experiments intended to demonstrate a violation usually require additional assumptions that make them vulnerable to a number of ``loopholes.'' In both pulsed and continuously pumped photonic experiments, an experimenter needs to identify which detected photons belong to the same pair, giving rise to the coincidence-time loophole. Here, via two different methods, we derive Clauser-Horne- and Eberhard-type inequalities that are not only free of the fair-sampling assumption (thus not being vulnerable to the detection loophole), but also free of the fair-coincidence assumption (thus not being vulnerable to the coincidence-time loophole). Both approaches can be used for pulsed as well as for continuously pumped experiments. Moreover, as they can also be applied to already existing experimental data, we finally show that a recent experiment [Giustina et al., Nature (London) 497, 227 (2013)] violated local realism without requiring the fair-coincidence assumption.
We report an Einstein-Podolsky-Rosen-Bohm experiment with a pulsed source of entangled pairs of photons, recording the time of arrival of the pulses and of the detection of each single photon. This allows varying the parameters of the analysis (as the size of the time coincidence window) at will after the experiment has ended. Among other results, we present the measurement of the time variation of the Clauser-Horne-Shimony-Holt parameter during the pulse. The obtained results close (or at least impose new and tight restrictions to) the last loophole that remains open in the tests of quantum mechanics vs local realism (the so-called coincidence loophole).
Experimental violations of Bell inequalities are in general vulnerable to so-called loopholes. In this work, we analyze the characteristics of a loophole-free Bell test with photons, closing simultaneously the locality, freedom-of-choice, fair-sampling (i.e., detection), coincidence-time, and memory loopholes. We pay special attention to the effect of excess predictability in the setting choices due to nonideal random-number generators. We discuss necessary adaptations of the Clauser-Horne and Eberhard inequality when using such imperfect devices and---using Hoeffding's inequality and Doob's optional stopping theorem---the statistical analysis in such Bell tests.
Recently, the results of the first experimental test for entangled photons closing the detection loophole (also referred to as the fair sampling loophole) were published (Vienna, 2013). From the theoretical viewpoint the main distinguishing feature of this long-aspired to experiment was that the Eberhard inequality was used. Almost simultaneously another experiment closing this loophole was performed (Urbana-Champaign, 2013) and it was based on the Clauser–Horne inequality (for probabilities). The aim of this note is to analyze the mathematical and experimental equivalence of tests based on the Eberhard inequality and various forms of the Clauser–Horne inequality. The structure of the mathematical equivalence is nontrivial. In particular, it is necessary to distinguish between algebraic and statistical equivalence. Although the tests based on these inequalities are algebraically equivalent, they need not be equivalent statistically, i.e., theoretically the level of statistical significance can drop under transition from one test to another (at least for finite samples). Nevertheless, the data collected in the Vienna test implies not only a statistically significant violation of the Eberhard inequality, but also of the Clauser–Horne inequality (in the ratio-rate form): for both a violation .
Recent experiments have reached detection efficiencies sufficient to close the detection loophole with photons. Both experiments ran multiple successive trials in fixed measurement configurations, rather than randomly re-setting the measurement configurations before each measurement trial. This opens a new potential loophole for a local hidden variable theory. The loophole invalidates one proposed method of statistical analysis of the experimental results, as demonstrated in this note. Therefore a different analysis will be necessary to definitively assert that these experiments are subject only to the locality loophole.
Bell's inequalities(1964) provides a quantitative criterion to test the local hidden variable theory(LHVT) versus quantum mechanics(QM).For the first time,it leads to the possibility to experimentally distinguish LHVT and QM.So far,there have been tens of experiments ever since the first experiment by Clauser et al(1972).An overwhelming majority of these experiments are in good agreement with the predictions of QM yet violate those of LHVT.Some loopholes in these experiments are discussed in Section I,followed by a respective summary to 12 experiments between 1972 to 1982 and 31 experiments from 1985 and on in Sections II and III.It is finally pointed out that so far there is not a single experiment to close both the locality loophole and the detection loophole at the same time,but the experimental outcomes are irreversible.Accordingly,theoretical physicists must admit that the present physics foundation is broken,i.e.quantum mechanics is contradiction with special relativity.