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.
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.
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 is really independent of the fair sampling assumption. For this purpose, we derive a more efficient Bell-type inequality which is a CHSH-type inequality in real experiments, using some alternative assumptions. Furthermore, Quantum mechanics violates our proposed inequality, In his celebrated 1964 paper, John Bell considered a system consisting of two spin-1 particles in a singlet state [1]. He showed that the correlation 2 between the results of two experiments done on such spatially separated particles
A recent experiment presented, for photons, the first violation of a Bell inequality closing the fair-sampling loophole, i.e., without having to assume that the sample of measured photons fairly represents the entire ensemble. In this note, we discuss a detailed quantum mechanical model for the experimental data. Within experimental error the experiment agrees with quantum mechanical prediction. We also discuss the effects of drifting laser intensity and show that it could not have mimicked a violation of the Bell inequality. Therefore, the experiment was immune to the "production-rate loophole."
Abstract Bell’s inequality provides a remarkable way to test the consistency between quantum mechanics and classic local realistic theory. However, experimental demonstrations of the loophole-free Bell test are challenging and only recently have been demonstrated with bipartite systems. A central obstacle for the photonic system is that the sampling efficiency, including the collection and detection efficiencies, must be above a certain threshold. We here generalize two-particle Eberhard’s inequality to the n-particle systems and derive a Bell-type inequality for multi-particle systems, which significantly relaxes this threshold. Furthermore, an experimental proposal to achieve a multi-partite Bell test without the fair sampling assumption is presented for the case of three particles. For any given value of the sampling efficiency, we give the optimal configurations for actual implementation, the optimal state, the maximum background noise that the system can tolerate, and the lowest fidelity of the quantum state. We believe our work can serve as a recipe for experimentalists planning to violate local realism using a multi-partite quantum state without the sampling loophole.
Almost all Bell inequality experiments to date have used postselection and therefore relied on the fair sampling assumption for their interpretation. The standard form of the fair sampling assumption is that the loss is independent of the measurement settings, so the ensemble of detected systems provides a fair statistical sample of the total ensemble. This is often assumed to be needed to interpret Bell inequality experiments as ruling out hidden-variable theories. Here we show that it is not necessary; the loss can depend on measurement settings, provided the detection efficiency factorizes as a function of the measurement settings and any hidden variable. This condition implies that Tsirelson's bound must be satisfied for entangled states. On the other hand, we show that it is possible for Tsirelson's bound to be violated while the Clauser-Horne-Shimony-Holt (CHSH)-Bell inequality still holds for unentangled states, and present an experimentally feasible example.
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.