Conclusive experimental tests of local realism deserve a minimum quantum efficiency in order to close detection loophole. This efficiency depends on the considered observables, on the specific Bell inequality chosen and on the dimension of the quantum objects observed. In this paper, we numerically analyse some quantum mechanics predictions on local realism for qubits, qutrits and ququats and we suggest a system to produce ququats maximally violating Bell-CGLMP inequality.
Conclusive experimental tests of local realism deserve a minimum quantum efficiency in order to close detection loophole. This efficiency depends on the considered observables, on the specific Bell inequality chosen and on the dimension of the quantum objects observed. In this paper, we numerically analyse some quantum mechanics predictions on local realism for qubits, qutrits and ququats and we suggest a system to produce ququats maximally violating Bell-CGLMP inequality.
Locality and realism are two main assumptions in deriving Bell's inequalities. Though the experimentally demonstrated violations of Bell's inequalities rule out local realism, it is, however, not clear what role each of the two assumptions solely plays in the observed violations. Here we show that two testable inequalities for the statistical predictions of two-qubit systems can be derived by assuming either locality or realism. It turns out that quantum mechanics respects a nonlocal classical realism, and it is locality that is incompatible with experimental observations and quantum mechanics.
Reliable and loophole-free demonstrations of the violation of local realism (LR) are highly desirable not only for understanding the foundation of quantum mechanics but also for facilitating quantum information processing, such as quantum key distribution and randomness expansion. To date, LR has been experimentally violated, but with loopholes, by testing predetermined Bell inequalities. This thesis presents a framework for verifying and quantifying the violation of LR without relying on a particular Bell inequality.\nFirst, the experimental resources, such as the quantum state, measurement settings, detection effciency, and visibility required for a violation of LR, are studied via a measure called the statistical strength. The higher the statistical strength, the more confidence in a violation of LR one has after a suffciently large number of experimental data. Particularly, we study the minimum detection effciency required to achieve any given statistical strength level in tests of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitter. It is shown that, compared with photon detectors, photon counters make violations of LR easier to detect for any nonzero probability of multiple photons in an output beam of the polarizing beam splitter.\nSecond, to quantify the statistical evidence against LR obtained from a finite number of experimental data, one can choose a test statistic, such as a Bell-inequality violation, to measure the amount of violation of LR. It is desirable to bound the probability, according to LR, of obtaining a test statistic at least as extreme as that observed. This probability is known as a p-value for the hypothesis test of LR. We propose a protocol to bound such a p-value. The bound provided is asymptotically tight, if the prepared quantum state and measurement settings are stable during an experiment. Therefore, the proposed protocol is asymptotically optimal, and the bound provided is a standardized measure of success for experimental tests of LR. One can quantitatively compare different experimental tests based on this bound. Moreover, the bound provided is valid even if the quantum state varies arbitrarily and local realistic models depend on previous measurement settings and outcomes. Hence, this bound facilitates device-independent and nonlocality-based quantum information processing. For comparison, bounds of p-values derived from Bell-inequality violations using the number of standard deviations of violation of a Bell inequality or using martingale theory are studied. It is found that putative bounds derived from the number of standard deviations of violation are not valid and bounds from martingale theory are not tight.\nFinally, a simplified and effcient data analysis protocol using a set of Bell inequalities is proposed and compared with the above optimal and martingale-based protocols. The simplified protocol provides as good as and typically tighter p-value bounds than the martingale-based protocol, and the bounds provided can even be asymptotically tight. Moreover, the simplified protocol can be applied to any test with linear witnesses, such as tests for verifying entanglement, system dimensionality, or steering.
Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.
Tests of local realism versus quantum mechanics based on Bell's inequality employ two entangled qubits. We investigate the general case of two entangled quantum systems defined in N-dimensional Hilbert spaces, or " quNits." Via a numerical linear optimization method we show that violations of local realism are stronger for two maximally entangled quNits ( 3</=N</=9) than for two qubits and that they increase with N. The two quNit measurements can be experimentally realized using entangled photons and unbiased multiport beam splitters.
Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect.
Quantum mechanics is strictly incompatible with local realism. It has been shown by Bell and others that it is possible, in principle, to experimentally differentiate between local realism and quantum mechanics. Numerous experiments have attempted to falsify local realism; however, they have consistently failed to close the detection loophole under strict locality conditions, thereby allowing local realistic explanations for their observations. In 2015, three experiments took place that tested local realism without the impediments of these significant loopholes. Between these three experiments, a substantial data set was collected. All of the collected data show a strong violation of local realism and strong support for quantum mechanics. This article reviews the theoretical basis of Bell tests and the affiliated loopholes, as well as the methods employed by these recent experiments and the implications of the results they observed. La mécanique quantique est strictement incompatible avec le réalisme local. Bell et d’autres scientifiques ont montré qu’il est possible, en théorie, de trouver la différence entre le réalisme local et la mécanique quantique expérimentalement. De nombreuses expériences ont tenté de falsifier le réalisme local; cependant, elles ont toujours échoué à combler la faille de détection dans des conditions de localité strictes, permettant ainsi des explications réalistes locales pour leurs observations. En 2015, trois expériences ont testé le réalisme local sans les entraves de ces failles importantes. Entre ces trois expériences, des données substantielles ont été recueillies. Toutes les données recueillies ont montré une forte déviation du réalisme local et un appui solid pour la mécanique quantique. Cet article examine les bases théoriques des tests de Bell et les failles af liées, ainsi que les méthodes employées par ces expériences récentes et les implications de leurs résultats.