We introduce an all-versus-nothing proof of impossibility of Einstein-Podolsky-Rosen's local elements of reality for two photons entangled both in polarization and path degrees of freedom, which leads to a Bell's inequality where the classical bound is 8 and the quantum prediction is 16. A simple estimation of the detection efficiency required to close the detection loophole using this proof gives eta > 0.69. This efficiency is lower than that required for previous proposals.
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…
Local realism is in conflict with special quantum Bell-type models. Recently, several experiments have demonstrated violation of local realism if we trust their setup assuming special relativity valid. In this paper we question the assumption of relativity, point out not commented anomalies and show that the experiments have not closed objectivity loophole because clonability of the result has not been demonstrated. We propose several improvements in further experimental tests of local realism make the violation more convincing.
It has long been known that the "detection loophole", present when detector efficiencies are below a critical figure, could open the way for alternative "local realist" explanations for the violation of Bell tests. It has in recent years become common to assume the loophole can be ignored, regardless of which version of the Bell test is employed. A simple model is presented that illustrates that this may not be justified. Two of the versions -- the standard test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at grave risk of bias. Statements implying that experimental …
Bell inequalities are intended to show that local realist theories cannot describe the world. A local realist theory is one where physical properties are defined prior to and independent of measurement, and no physical influence can propagate faster than the speed of light. Quantum-mechanical predictions for certain experiments violate the Bell inequality while a local realist theory cannot, and this shows that a local realist theory cannot give those quantum-mechanical predictions. However, because of unexpected circumstances or "loopholes" in available experiment tests, local realist theorie…
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 chal…
We introduce a new interpretation of quantum mechanics by examining the Einstein, Podolsky and Rosen's (EPR) paradox and Bell's inequality experiments under the assumption that the vacuum has an inhomogeneous texture for energy levels below the Heisenberg time-energy uncertainty relation. In this article, selected results from the most reliable Bell's inequality experiments will be quantitatively analyzed to show that our interpretation of quantum mechanics creates a new loophole in Bell's inequality, and that the past experimental findings do not contradict our new interpretation. Under the v…
We show all-versus-nothing proofs of Bell's theorem in the one-dimensional transverse-field Ising model, which is one of the most important exactly solvable models in the field of condensed matter physics. Since this model can be simulated with nuclear magnetic resonance, our work might lead to a fresh approach to experimental test of the Greenberger-Horne-Zeilinger contradiction between local realism and quantum mechanics.
We develop and exploit a source of two-photon four-dimensional entanglement to report the first two-particle all-versus-nothing test of local realism with a linear optics setup, but without resorting to a non-contextuality ssumption. Our experimental results are in well agreement with quantum mechanics while in extreme contradiction with local realism. Potential applications of our experiment are briefly discussed.
Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)^2 for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After…
We present a loophole-free violation of local realism using entangled photon pairs. We ensure that all relevant events in our Bell test are spacelike separated by placing the parties far enough apart and by using fast random number generators and high-speed polarization measurements. A high-quality polarization-entangled source of photons, combined with high-efficiency, low-noise, single-photon detectors, allows us to make measurements without requiring any fair-sampling assumptions. Using a hypothesis test, we compute p-values as small as $5.9\times 10^{-9}$ for our Bell violation while maint…
Recently much interest has been directed towards designing setups that achieve realistic loss thresholds for decisive tests of local realism, in particular in the optical regime. We analyse the feasibility of such Bell tests based on a W-state shared between multiple parties, which can be realised for example by a single photon shared between spatial modes. We develop a general error model to obtain thresholds on the efficiencies required to violate local realism, and also consider two concrete optical measurement schemes.
We introduce a two-observer all-versus-nothing proof of Bell's theorem which reduces the number of required quantum predictions from 9 [A. Cabello, Phys. Rev. Lett. 87, 010403 (2001); Z.-B. Chen et al., Phys. Rev. Lett. 90, 160408 (2003)] to 4, provides a greater amount of evidence against local realism, reduces the detection efficiency requirements for a conclusive experimental test of Bell's theorem, and leads to a Bell's inequality which resembles Mermin's inequality for three observers [N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990)] but requires only two observers.
The usual entanglement swapping protocol can entangle two particles that never interact. Here we demonstrate an all-versus-nothing violation of local realism for a partial entanglement swapping process. A Clauser-Horne-Shimony-Holt-type inequality for two particles entangled by entanglement swapping is proposed for a practical experiment and can be violated quantum mechanically up to 4 beyond Cirel'son's bound 2sqr(2). Our result uncovers the intriguing nonlocal character of entanglement swapping and may lead to a conclusive (loophole-free) test of local realism versus quantum mechanics. The e…
We introduce two two-player quantum pseudo-telepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Methot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light-cone (quant-ph/0511047) is incorrect.
Assuming perfect detection efficiency, we present an (indeterministic) model for an EPR-Bohm experiment which reproduces the singlet correlations, without contradicting Bell's original locality condition. In this model we allow the probability distribution $ρ_λ$ of the state $λ$ at the source to depend parametrically on the orientation $ξ$ of one of the measuring devices: $ρ_λ(λ,ξ)$. In a Bell experiment, no-signaling between the source and each one of the devices would seem clearly sufficient to rule such an influence; however, not even schemes where the choice of observables takes place duri…
We investigate the nonlocal property of the fractional statistics in Kitaev's toric code model. To this end, we construct the Greenberger-Horne-Zeilinger paradox which builds a direct conflict between the statistics and local realism. It turns out that the fractional statistics in the model is purely a quantum effect and independent of any classical theory.We also discuss a feasible experimental scheme using anyonic interferometry to test this contradiction.
I purport to show why old and new claims on the role of counterfactual reasoning for the EPR argument and the Bell theorem are unjustified: once the logical relation between locality and counterfactual reasoning is clarified, the use of the latter does no harm and the nonlocality result can well follow from the EPR premises. To show why, I critically review (i) incompleteness arguments that Einstein developed before the EPR paper, and (ii) more recent claims that equate the use of counterfactual reasoning with the assumption of a strong form of realism.
In a local realist world view, 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 within local realism. Such experiments usually require additional assumptions that make them vulnerable to a number of "loopholes." A recent experiment [Giustina et al, Nature, 2013] violated a Bell inequality without being vulnerable to the detection (or fair-sampling) loophole, therefore not needing the fair-sampling assump…
It is currently widely accepted, as a result of Bell's theorem and related experiments, that quantum mechanics is inconsistent with local realism and there is the so called quantum non-locality. We show that such a claim can be justified only in a simplified approach to quantum mechanics when one neglects the fundamental fact that there exist space and time. Mathematical definitions of local realism in the sense of Bell and in the sense of Einstein are given. We demonstrate that if we include into the quantum mechanical formalism the space-time structure in the standard way then quantum mechan…
It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized to the case with only two entangled particles. The reasoning makes use of two photons which are maximally entangled both in polarization and in spatial degrees of freedom. In contrast to Cabello's argument of "all versus nothing" nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)], our proposal to test the theorem can be implemented with linear optics and thus is well within the reach of current experimental technology.
Hardy's is one of the simplest arguments concerning non-locality. Recently Chen et. al. have proposed a more generalized Hardy-like argument and have shown that the probability of success increases with local system's dimension. Here we study the same in a minimally constrained theory, namely the generalized no-signaling theory(GNST). We find that not only the probability of success of this argument increases with local system dimension in GNST, it also takes a very simple functional form.
The conjecture is made that quantum mechanics is compatible with local hidden variables (or local realism). The conjecture seems to be ruled out by the theoretical argument of Bell, but it is supported by the empirical fact that nobody has been able to perform a loophole-free test of local realism in spite of renewed effort during almost 40 years.
We discuss the problem of finding the most favorable conditions for closing the detection loophole in a test of local realism with a Bell inequality. For a generic non-maximally entangled two-qubit state and two alternative measurement bases we apply Hardy's proof of non-locality without inequality and derive an Eberhard-like inequality. For an infinity of non-maximally entangled states we find that it is possible to refute local realism by requiring perfect detection efficiency for only one of the two measurements: the test is free from the detection loophole for any value of the detection ef…
We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure of local realism can be manifested by exploiting wave and particle correlations of readily accessible continuous-variable states, with very large violation of inequalities insensitive to detector-efficiency, which makes a strong case for a loophole-free test.
In a recent article Giustina et al. [Phys. Rev. Lett. 115, 250401 (2015)] report on an advanced Bell experiment, simultaneously closing loopholes for local hidden-variable theories. The authors claim that 'local realism' has been refuted, unless 'truly exotic hypotheses' are made. Here I argue that a particularly wide and natural class of local hidden-variable theories survives, for instance when the hidden variables describe a background field. Such background-based theories exploit the freedom-of-choice loophole, which cannot be closed for this type of hidden variables. The dynamics of such …
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-o…
We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell's inequality tests, in a specific Hardy-type experiment. Hardy's contradiction without inequalities between Local Realism and Quantum Mechanics can be translated into a feasible experiment by requiring ideal detection efficiencies for only one of the observables to be alternatively measured. Neutral kaons are near to fulfil this requirement and therefore to close the efficiency loophole.
We demonstrate extraction of randomness from spontaneous-emission events less than 36 ns in the past, giving output bits with excess predictability below $10^{-5}$ and strong metrological randomness assurances. This randomness generation strategy satisfies the stringent requirements for unpredictable basis choices in current "loophole-free Bell tests" of local realism [Hensen et al., Nature (London) 526, 682 (2015); Giustina et al., Phys. Rev. Lett. 115, 250401 (2015); Shalm et al., Phys. Rev. Lett. 115, 250402 (2015)].
Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumpt…
It is argued that local realism is a fundamental principle, which might be rejected only if experiments clearly show that it is untenable. A critical review is presented of the derivations of Bell's inequalities and the performed experiments, with the conclusion that no valid, loophole-free, test exists of local realism vs. quantum mechanics. It is pointed out that, without any essential modification, quantum mechanics might be compatible with local realism. This suggests that the principle may be respected by nature.
We present a source of entangled photons that violates a Bell inequality free of the "fair-sampling" assumption, by over 7 standard deviations. This violation is the first experiment with photons to close the detection loophole, and we demonstrate enough "efficiency" overhead to eventually perform a fully loophole-free test of local realism. The entanglement quality is verified by maximally violating additional Bell tests, testing the upper limit of quantum correlations. Finally, we use the source to generate secure private quantum random numbers at rates over 4 orders of magnitude beyond prev…
In a recent article Hensen et al. [Nature 526, 682 (2015)] report on a sophisticated Bell experiment, simultaneously closing, for the first time, loopholes for local hidden-variable theories (HVTs). The authors claim that 'local realism' has been refuted, under certain natural assumptions. The aim of the present Comment is twofold. First, it is urged that the class of local HVTs that is eliminated by the reported experiment should be specified in greater detail than is done by the authors. Second, it is argued that the class of local HVTs that still survives is wide and natural. For instance, …
Because of the fundamental importance of Bell's theorem, a loophole-free demonstration of a violation of local realism (LR) is highly desirable. Here, we study violations of LR involving photon pairs. We quantify the experimental evidence against LR by using measures of statistical strength related to the Kullback-Leibler (KL) divergence, as suggested by van Dam et al. [W. van Dam, R. Gill and P. Grunwald, IEEE Trans. Inf. Theory. 51, 2812 (2005)]. Specifically, we analyze a test of LR with entangled states created from two independent polarized photons passing through a polarizing beam splitt…
An experimental test of Bell's inequality allows ruling out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of spacelike separation between the measurement events. Only very recently could both loopholes be closed simultaneously. Here we present a statistically significant, event-ready Bell test based on combining heralded entanglement of atoms separated by $398\,\mathrm{m}$ with fast an…
Closing objectivity loophole in Bell tests on a public quantum computer
University of Warsaw（华沙大学）；Departament de Física and Institut d’Aplicacions Computacionals de Codi Comunitari (IAC3)（物理系与通用代码计算应用研究所（IAC3））；CRISP – Centre de Recerca Independent de sa Pobla（萨波布拉独立研究中心（CRISP））；University of Lodz（罗兹大学）；Center for Theoretical Physics, Polish Academy of Sciences（波兰科学院理论物理中心）
I point out critical errors in the paper "Bell's Theorem Versus Local Realism in a Quaternionic Model of Physical Space" by J. Christian, published in IEEE Access. Christian's paper in fact contains several conflicting models. None of them form counterexamples to Bell's theorem. Most of Christian's paper is devoted to a model based on the detection loophole due to Pearle (1970).
This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experime…
Fundamental principle of classical physics -- local realism, means that freely chosen observations can be explained by a local (slower than light) real process. It is apparently violated in quantum mechanics as shown by Bell theorem. Despite extreme efforts experiments have not conclusively confirmed this violation due to loopholes. We propose a new postulate that the description of quantum processes must be consistent with local realism, It also assumes existence of many worlds/copies of the same system, interacting weakly microscopically but strongly macroscopically, whose number can be esti…
A classical model is presented for the features of parametric down-conversion and homodyne detection relevant to recent proposed ``loophole-free'' Bell tests. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If cit is not, then the experiments will fail in their initial concept, since both quantum theorists and local r…
Loophole-free experiments have demonstrated that at least one of three features is false when the violation of Bell's inequalities is observed: Locality, Realism or (what is lesser known) Ergodicity. An experiment is proposed to find out, or at least to get an indication about, which one is false. It is based on recording the time evolution of the rate of series of outcomes that are found not-random in a pulsed Bell's setup. The results of such experiment would be important not only to the foundations of Quantum Mechanics. For, even if the foundational issue remained not fully decided, they wo…
A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrar…
For more than 80 years, the counterintuitive predictions of quantum theory have stimulated debate about the nature of reality. In his seminal work, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory. Bell showed that in any local realist theory the correlations between distant measurements satisfy an inequality and, moreover, that this inequality can be violated according to quantum theory. This provided a recipe for experimental tests of the fundamental principles underlying the laws of nature. In the past decades, num…
Recent proposed ``loophole-free'' Bell tests are discussed in the light of classical models for the relevant features of optical parametric amplification and homodyne detection. The Bell tests themselves are uncontroversial: there are no obvious loopholes that might cause bias and hence, if the world does, after all, obey local realism, no violation of a Bell inequality will be observed. Interest centres around the question of whether or not the proposed criterion for ``non-classical'' light is valid. If it is not, then the experiments will fail in their initial concept, since both quantum the…
In this paper we describe a test of Bell inequalities using a non- maximally entangled state, which represents an important step in the direction of eliminating the detection loophole. The experiment is based on the creation of a polarisation entangled state via the superposition, by use of an appropriate optics, of the spontaneous fluorescence emitted by two non-linear crystals driven by the same pumping laser.
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with them. The Bell-Kochen-Specker theorem states that noncontextual realism cannot reproduce the measurement statistics of a single three-level quantum system (qutrit). Noncontextual realistic models may thus be tested using a single qutrit without relying on the notion of quantum entanglement in contrast to Bell inequality tests. It is challenging to refute such …
Recently, a group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all of the experiments. Among these assumptions are fair sampling, no signaling, and faithful reproduction of a Bell-type quantum model. We examined the data from 9 of 13 experiments and analyzed occurring anomalies in view of the above assumptions. We conclude that further tests of local realism need better setup calibration to avoid apparent signaling or necessity of the complicated u…
We discuss the recently observed "loophole free" violation of Bell's inequalities in the framework of a physically realist view of quantum mechanics, which requires that physical properties are attributed jointly to a system, and to the context in which it is embedded. This approach is clearly different from classical realism, but it does define a meaningful "quantum realism" from a general philosophical point of view. Consistently with Bell test experiments, this quantum realism embeds some form of non-locality, but does not contain any action at a distance, in agreement with quantum mechanic…
In any Bell test, loopholes can cause issues in the interpretation of the results, since an apparent violation of the inequality may not correspond to a violation of local realism. An important example is the coincidence-time loophole that arises when detector settings might influence the time when detection will occur. This effect can be observed in many experiments where measurement outcomes are to be compared between remote stations because the interpretation of an ostensible Bell violation strongly depends on the method used to decide coincidence. The coincidence-time loophole has previous…
Quantum correlations are critical to our understanding of nature, with far-reaching technological and fundamental impact. These often manifest as violations of Bell's inequalities, bounds derived from the assumptions of locality and realism, concepts integral to classical physics. Many tests of Bell's inequalities have studied pairs of correlated particles; however, the immense interest in multi-particle quantum correlations is driving the experimental frontier to test systems beyond just pairs. All experimental violations of Bell's inequalities to date require supplementary assumptions, openi…
Bell's theorem is based on three assumptions: realism, locality, and measurement independence. The third assumption is identified by Bell as linked to the freedom of choice hypothesis. He holds that ultimately the human free will can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this third assumption are known in the literature as "freedom-of-choice loophole" (FOCL). In a recent publication, Abellán et al [2018] address this problem and follow this same strategy embraced by Bell [2004]. Nevertheless, the possibility of human freedom of ch…
We analyze the validity of Bell and Kochen-Specker theorems under local (or noncontextual) realism but avoiding an assumption of the existence of a joint probability distribution for incompatible observables. We formulate a realist model which complies with this requirement. This is obtained by employing divergent sequences that nevertheless have marginals which are convergent. We find that under standard reasonable assumptions this possibility does not lead to a loophole of those theorems, by deriving a short of CHSH inequality valid for any finite size ensemble. Moreover, we analyze a Hardy'…
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be defined as the maximum probability according to local realism of a violation at least as high as that witnessed. Thus, high violation corresponds to small p-value. We propose a prediction-based-ratio (PBR) analysis protocol whose p-values are valid even if the prepared quantum state varies arbitrarily and local realistic models can depend on previous measurem…
Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory - nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of …
