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arXiv:quant-ph/0306045

Testing the Fair Sampling Assumption for EPR-Bell Experiments with Polarizer Beamsplitters

Guillaume Adenier, Andrei Yu. Khrennikov

Published Jun 5, 2003• 1 citation
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Abstract

In spite of many attempts, no local realistic model seems to be able to reproduce EPR-Bell type correlations, unless non ideal detection is allowed. The low efficiency of detectors in all experiments with photons makes the use of the fair sampling assumption unavoidable. However, since this very assumption is false in all existing local realistic models based on inefficient detection, we thus question its validity. We show that it is no more reasonable to assume fair sampling than it is impossible to test, and we actually propose an experimental test which would provides clear cut results in case of unfair sampling.

DOI
10.48550/arxiv.quant-ph/0306045

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In spite of many attempts, no local realistic model seems to be able to reproduce EPR-Bell type correlations, unless non ideal detection is allowed. The low efficiency of detectors in all experiments with photons makes the use of the fair sampling assumption unavoidable. However, since this very assumption is false in all existing local realistic models based on inefficient detection, we thus question its validity. We show that it is no more reasonable to assume fair sampling than it is impossible to test, and we actually propose an experimental test which would provides clear cut results in case of unfair sampling.
Summary form only given. In a Bell experiment, one prepares pairs of entangled particles and sends them to two observers, Alice and Bob, for measurement and detection [1]. For some choices of their measurement settings, Alice and Bob may observe strong correlations between their results in accordance with the predictions of quantum mechanical theory. Conversely, any physical theory that assumes no physical influence can be faster than the speed of light and that properties of physical systems are elements of reality [2] - a local realistic theory - can predict only a limited amount of correlation between Alice's and Bob's measurement outcomes. Upon observing correlations sufficient to violate Bell's inequality, Alice and Bob must abandon local realism.It is common that in an experiment, some particles emitted by the source will not be detected. Then the subset of detected particles might display correlations that violate the Bell inequality although the entire ensemble can be described by a local realistic theory [3]. To achieve a conclusive Bell violation without assuming that the detected particles are a “fair” sample, a highly efficient setup is necessary. Due to experimental limitations, fair sampling has been assumed in most Bell experiments performed to date, and it has never been possible to avoid this assumption with photons due to the absence of efficient sources and detectors. Here we report the first Bell experiment with photons that does not rely on any fair-sampling assumption. In our experiment we employ the Eberhard inequality, a Bell inequality that by construction does not rely on the fair-sampling assumption [4]. Our source of entangled photon pairs utilizes bulk-crystal spontaneous parametric downconversion in a Sagnac configuration, which has shown to be very efficient [5, 6]. For photon detection, we employ superconducting transition-edge sensors, which not only offer high efficiency but also are intrinsically free of dark counts [7]. This combination of features is imperative for an experiment in which no correction of count rates can be tolerated. We achieve uncorrected coupling efficiencies over 73% in each arm of our source, facilitating a violation of the inequality by nearly 70 standard deviations after five minutes of measurement. Since the first experimental Bell test, a satisfactory laboratory realization of the motivating gedankenexperiment has remained an outstanding challenge. The two other main assumptions include “locality” [8, 9] and “freedom of choice” [10]. Invoking any of these renders an experiment vulnerable to explanation by a local realistic theory. The realization of an experiment that is free of all three assumptions-a so-called loopholefree Bell test-remains an important outstanding goal for the physics community with strong implications for quantum technologies. We note that with our experiment, photons are the first physical system for which each of these three assumptions has been successfully addressed, albeit in different experiments. This represents promise for practical applications like one-sided device-independent quantum key distribution [11], and in an additional test, we also demonstrate that our experimental apparatus is capable of implementing this protocol on both sides.
Bell inequalities applicable to non-ideal EPRB experiments are critical to the interpretation of experimental Bell tests. In this article it is shown that previous treatments of this subject are incorrect due to an implicit assumption and new inequalities are derived under general conditions. Published experimental evidence is reinterpreted under these results and found to be entirely compatible with local-realism, both, when experiments involve inefficient detection, if fair-sampling detection is assumed, as well as when experiments have nearly ideal detection and measurement crosstalk is taken into account.
We analyse optical EPR experimental data performed by Weihs et al in Innsbruck 1997–1998. We show that for some linear combinations of the raw coincidence rates, the experimental results display some anomalous behaviour that a more general source state (like non-maximally entangled state) cannot straightforwardly account for. We attempt to explain these anomalies by taking account of the relative efficiencies of the four channels. For this purpose, we use the fair sampling assumption, and assume explicitly that the detection efficiencies for the pairs of entangled photons can be written as a product of the two corresponding detection efficiencies for the single photons. We show that this explicit use of fair sampling cannot be maintained to be a reasonable assumption as it leads to an apparent violation of the no-signalling principle.
In the experimental verification of Bell's inequalities in real photonic experiments, it is generally believed that the so-called fair sampling assumption (which means that a small fraction of results provide a fair statistical sample) has an unavoidable role. Here, we want to show that the interpretation of these experiments could be feasible, if some different alternative assumptions other than the fair sampling were used. For this purpose, we derive an efficient Bell-type inequality which is a CHSH-type inequality in real experiments. Quantum mechanics violates our proposed inequality, independent of the detection-efficiency problems.