A certain class of parametric down-conversion Bell-type experiments has the following features. In the idealized perfect situation it is in only 50% of the cases that each observer receives a photon; in the other $50%$ one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts about whether such experiments could ever be genuine tests of local realism. We propose to take into account these ``unfavorable'' cases and to analyze the entire pattern of polarization and localization correlations. This departure from the standard reasoning enables one to show that the experiments are indeed a true test of local realism.
A certain class of parametric down-conversion Bell-type experiments has the following features. In the idealized perfect situation it is in only 50% of the cases that each observer receives a photon; in the other 50 one observer receives both photons of a pair while the other observer receives none. The standard approach is to discard the events of the second type. Only the remaining ones are used as the data input to some Bell inequalities. This raises justified doubts about whether such experiments could ever be genuine tests of local realism. We propose to take into account these ``unfavorable'' cases and to analyze the entire pattern of polarization and localization correlations. This departure from the standard reasoning enables one to show that the experiments are indeed a true test of local realism.
In recent years parametric-down-conversion photon sources have been proposed and used to test local realism via Bell-type inequalities. This study shows that this technique fails to discriminate between quantum mechanics and local realism in all those tests in which polarization correlations are measured, since dichotomic observables cannot be associated satisfactorily with the state produced in these experiments. A more adequate description of these photon sources leads to an alternative inequality for Einstein locality, which is always satisfied by quantum-mechanical predictions. The result can be extended to all the experiments in which only one-half of the emitted pairs are detected.
Conventional tests of Bell’s inequality rely on entangled photon pairs. Here, we replace entangled pairs with two independent photons of orthogonal polarization, and demonstrate that Bell’s inequality is still violated. Given the inherent local realism of independent photons, this experiment proves that Bell’s inequality cannot falsify the local realism of photons. We thus conjecture that the violation of Bell’s inequality by entangled photon pairs originates from their orthogonal polarizations, rather than the breakdown of local realism. To interpret this unexpected violation with independent photons, we further substitute the two photons with two monochromatic light beams, and calculate the transmittance correlation through polarizers via Malus’s law and Karl Pearson’s correlation formula. We show that this correlation also defies Bell’s inequality. Retracing the derivation of Bell’s inequality reveals its validity is restricted to binary events, which accounts for the observed violation with light beams. Finally, we propose a thought experiment involving gradual attenuation of light intensity down to the single-photon regime, and hypothesize that single-photon transmission through a polarizer does not constitute a binary event. This hypothesis provides a unified interpretation for both our experimental findings and all canonical Bell inequality tests reported to date.
Spontaneous parametric down-conversion is a convenient source of pairs of entangled photons. Within special interferometric configurations involving either two sources of this kind or double emissions from such a source, one can observe three-photon Greenberger-Horne-Zeilenger--type interference effects. Unfortunately, events of some other types necessarily occur. It is shown that under specific operational conditions, thus far not met by the experiments, the entirety of the phenomena observed in such experiments has no local realistic model. However, one can show this only by analyzing the entire pattern of all events predicted by quantum mechanics.
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.
We have performed a test of local realism using entangled photons produced by spontaneous parametric downconversion. This experimental test is based on an idea originally proposed by Hardy for a test of local realism without inequalities, although our experiment actually measures an inequality (as any experiment must). We find a more-than-70 standard deviation violation of the predictions of local realism. The experimental effort required for this test is essentially the same as that required for a test of a Bell inequality. However, this test is based on concepts that are easier to understand and more compelling than those behind the original Bell inequality.
The nonlocality inherent in quantum mechanics has been tested experimentally, but the nonlocal interpretation of all the relevant experiments can be challenged. All past tests of Bell's inequalities have required supplementary assumptions, without which the experimental results satisfy the inequalities, in agreement with the notion of local realism. There are basically three loopholes that need to be closed; neither the cascade sources nor the parametric down-conversion sources of correlation photons used to date are capable of closing all of them, even if the detectors used had been 100% efficient. We propose a two-crystal down-conversion source, relying on type-II collinear phase matching, which should permit a violation of Bell's inequalities without the need for supplementary assumptions. As the source can produce a true singletlike state, it is also relevant for quantum cryptographic applications.