Miguel Socolovsky
We review the theorems of Einstein-Podolsky-Rosen (EPR), Bell, Greenberger-Horne-Zeilinger (GHZ), and Hardy, and present arguments supporting the idea that quantum mechanics is a complete, causal, non local, and non separable theory.
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We propose here an experimental test of the fair sampling assumption in two-channel EPR-Bell experiments for which the detection loophole holds.
A mathematical rigorous definition of EPR states has been introduced by Arens and Varadarajan for finite dimensional systems, and extended by Werner to general systems. In the present paper we follow a definition of EPR states due to Werner. Then we show that an EPR state for incommensurable pairs is Bell correlated, and that the set of EPR states for incommensurable pairs is norm dense between two strictly space-like separated regions.
A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive inference and Einstein separability.
A conjecture concerning vacuum correlations in axiomatic quantum field theory is proved. It is shown that this result can be applied both in the context of EPR-type experiments and Bell-type experiments.
Bell nonlocality and Einstein-Podolsky-Rosen (EPR) steering are every important quantum correlations of a composite quantum system. Bell nonlocality of a bipartite state is a quantum correlation demonstrated by some local quantum measurements, while EPR steering is another form of quantum correlations, observed firstly by Schrodinger in the context of famous EPR paradox. In this paper, we give some remarks on Bell nonlocality and EPR steering of bipartite states, including mathematical definitions and characterizations of these two quantum correlations, the convexity and closedness of the set …
The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.
A generalized form of EPR state is defined, embracing both classical and nonclassical states. It is shown that for such states, Bell's inequality is equivalent to a constraint on stochastic field theories. Thus, violation of Bell's inequality can be observed also for weak violation of stochastic field theories. The Schrodinger cat state is shown to be an example of this.
According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual 'violation' of Bell inequality to a 'non-violation' for times larger than a characteristic time scale which…
Bell-EPR Correlations within Local Quantum Theory
本文提出一种局部幺正理论，通过预测量过滤单光子偏振并结合四个光电探测器的检测过程，解释贝尔-爱因斯坦-波多尔斯基-罗森相关性，强调本地去相干与非本地解释的差异。
We discuss supplementary (or hidden) variables in spin-measuring equipments in EPR-Bell experiment. This theme was considered in a Bell's later work. We generalize it. First, we show why the original supplementary variable $λ$ is not to be regarded to include supplementary variables in spin-measuring equipments (why supplementary variables should be introduced additionally in spin-measuring equipments) Next, we show the followings. When the supplementary variables introduced in spin-measuring equipments have local correlations, the Bell inequality is recovered. On the other hand, when they hav…
The question has been solved whether Bell's inequalities cover all possible kinds of hidden-variable theories. It has been shown that the given nequalities can be hardly derived when the changing space position of photon-pair source together with the microscopic space structure of measuring devices are taken into account; and when corresponding impact parameters (i.e., exact impact points) of photons in individual measuring devices (polarizers) influence measured values, in addition to usually considered characteristics.
We show that paradoxical consequences of violations of Bell's inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities which only partially define a probability space. Ignoring this conditioning leads to apparent contradictions in the classical probabilistic model (due to Kolmogorov). We show how to make a completely cons…
Entanglement is the defining feature of quantum mechanics, and understanding the phenomenon is essential at the foundational level and for future progress in quantum technology. The concept of steering was introduced in 1935 by Schrödinger as a generalization of the Einstein-Podolsky-Rosen (EPR) paradox. Surprisingly, it has only recently been formalized as a quantum information task with arbitrary bipartite states and measurements, for which the existence of entanglement is necessary but not sufficient. Previous experiments in this area have been restricted to the approach of Reid [PRA 40, 91…
Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden …
The best case for thinking that quantum mechanics is nonlocal rests on Bell's Theorem, and later results of the same kind. However, the correlations characteristic of EPR-Bell (EPRB) experiments also arise in familiar cases elsewhere in QM, where the two measurements involved are timelike rather than spacelike separated; and in which the correlations are usually assumed to have a local causal explanation, requiring no action-at-a-distance. It is interesting to ask how this is possible, in the light of Bell's Theorem. We investigate this question, and present two options. Either (i) the new cas…
Past, present and future experimental tests of quantum nonlocality are discussed. Consequences of assuming that the state-vector collapse is a real physical phenomenon in space-time are developed. These lead to experiments feasible with today's technology.
We give a analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just correspond to Tsirelson bound of Bell inequality, and the upper bound of Hardy's non-locality allowed by the principle of no-signaling just correspond to the algebraic maximum of Bell operator. Then we study the Cabello's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and vi…
Quantum nonlocality has recently been classified into three distinct types: quantum entanglement, Einstein-Podolsky-Rosen (EPR) steering, and Bell's nonlocality. Experimentally Bell's nonlocality is usually tested by quantum violation of the Clause-Horne-Shimony-Holt (CHSH) inequality in the two-qubit system. Bell's nonlocality is the strongest type of nonlocality, also due this reason Bell-test experiments have encountered both the locality loophole and the detection loophole for a very long time. As a weaker nonlocality, EPR steering naturally escapes from the locality loophole and is corres…
We show that the projection postulate plays a crucial role in the discussion on the so called "quantum nonlocality", in particular in the EPR-argument. We stress that the original von Neumann projection postulate was crucially modified by extending it to observables with degenerate spectra (the Lüders postulate) and we show that this modification is highly questionable from a physical point of view, and it is the real source of "quantum nonlocality". The use of the original von Neumann postulate eliminates this problem: instead of "action at the distance"-nonlocality, we obtain a classical mea…
A local theory with a local correlation is proposed to give an explanation for the contractions in the GHZ-like proofs for Bell's theorem and the violation to Bell's inequality. It agrees with the experimental predictions for the GHZ state of three entangled spins, the Bell state of two entangled spins and one spin state. It is found that the contradiction in the GHZ-like proofs and the violation to Bell's inequality can be attributed to the local correlation.
In this paper we identify a hidden premise in Bell's theorem: measurability of the underlying space. But our system (the space of all paths, SP) is not measurable, although it replicates the predictions of standard quantum mechanics. Using it we present three counterexamples to Bell's theorem and also show why Bell-like arguments for more than two particles cannot be carried out in this model. Moreover, we show that the result places severe constraints on possible viable interpretations of quantum mechanics: Either an interpretation must in some form represent a quantum system in terms of all …
We analyse notion of independence in the EPR-Bohm framework by using comparative analysis of independence in conventional and frequency probability theories. Such an analysis is important to demonstrate that Bell's inequality was obtained by using totally unjustified assumptions (e.g. the Bell-Clauser-Horne factorability condition). Our frequency analysis also demonstrated that Gill-Weihs-Zeilinger-Zukowski's arguments based on "the experimenter's freedom to choose settings" to support the standard Bell approach are neither justified by the structure of the EPR-Bohm experiment. Finally, our an…
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 c…
Maudlin has claimed that no local theory can reproduce the predictions of standard quantum mechanics that violate Bell's inequality for Bohm's version (two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen problem. It is argued that, on the contrary, standard quantum mechanics itself is a counterexample to Maudlin's claim, because it is local in the appropriate sense (measurements at one place do not influence what occurs elsewhere there) when formulated using consistent principles in place of the inconsistent appeals to "measurement" found in current textbooks. This argum…
A new formulation of the EPR argument is presented, one which uses John Bell's mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR bears a striking resemblance to Bell's derivation of his famous inequalities. The relation between these two arguments -- in particular, the role of EPR as part one of Bell's two-part argument for nonlocality -- is also discussed in detail.
In this contribution I will review the analysis of the Einstein-Podolsky-Rosen argument, Bell's inequalities and of associated experiments for spins in terms of positive operator valued measures. Specifically, I will explore the relation between the Clauser-Horne-Shimony-Holt inequality and a fundamental \emph{classicality} property of observables -- their \emph{coexistence}. A derivation of Bell's inequalities for unsharp spins will be given which follows a reconstruction by Mittelstaedt and Stachow of the original EPR argument. In this context we discuss the need for a consistent relativisti…
Bell and EPR experiments with signalling data
本文提出扩展局部隐变量和隐状态理论以允许有限信号，通过精确方法和修正贝尔不等式来测试非经典性，并通过IBM量子处理器和低效率探测器数据验证其适用性。
It is shown that Bell's proof of violation of local realism in phase space is incorrect. Using Bell's approach, a violation can be derived also for nonnegative Wigner distributions. The error is found to lie in the use of an unnormalizable Wigner function.
We discuss the problem of finding a Lorentz invariant extension of Bohmian mechanics. Due to the nonlocality of the theory there is (for systems of more than one particle) no obvious way to achieve such an extension. We present a model invariant under a certain limit of Lorentz transformations, a limit retaining the characteristic feature of relativity, the non-existence of absolute time resp. simultaneity. The analysis of this model exemplifies an important property of any Bohmian quantum theory: the quantum equilibrium distribution $ρ= |ψ|^2$ cannot simultaneously be realized in all Lorentz …
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
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…
We give a simple non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality, also known as local causality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.
Local realistic models cannot completely describe all predictions of quantum mechanics. This is known as Bell's theorem that can be revealed either by violations of Bell inequality, or all-versus-nothing proof of nonlocality. Hardy's paradox is an important all-versus-nothing proof and is considered as "the simplest form of Bell's theorem". In this work, we theoretically build the general framework of Hardy-type paradox based on Bell inequality. Previous Hardy's paradoxes have been found to be special cases within the framework. Stronger Hardy-type paradox has been found even for the two-qubit…
Tests such as Bell's inequality and Hardy's paradox show that joint probabilities and correlations between distant particles in quantum mechanics are inconsistent with local realistic theories. Here we experimentally demonstrate these concepts in the time domain, using a photonic entangling gate to perform nondestructive measurements on a single photon at different times. We show that Hardy's paradox is much stronger in time and demonstrate the violation of a temporal Bell inequality independent of the quantum state, including for fully mixed states.
We present a detailed analysis of assumptions that J. Bell used to show that local realism contradicts QM. We find that Bell's viewpoint on realism is nonphysical, because it implicitly assume that observed physical variables coincides with ontic variables (i.e., these variables before measurement). The real physical process of measurement is a process of dynamical interaction between a system and a measurement device. Therefore one should check the adequacy of QM not to ``Bell's realism,'' but to adaptive realism (chameleon realism). Dropping Bell's assumption we are able to construct a natur…
We present comparative analysis of Gill-Weihs-Zeilinger-Zukowski arguments directed against Hess-Philipp anti-Bell arguments. In general we support Hess-Philipp viewpoint to the sequence of measurements in the EPR-Bohm experiments as stochastic time-like process. On the other hand, we support Gill-Weihs-Zeilinger-Zukowski arguments against the use of time-like correlations as the factor blocking the derivation of Bell-type inequalities. We presented our own time-analysis of measurements in the EPR-Bohm experiments based on the frequency approach to probability. Our analysis gives strong argume…
We begin with a review of the famous thought experiment that was proposed by Einstein, Podolsky and Rosen (EPR) and mathematically formulated by Bell; the outcomes of which challenge the completeness of quantum mechanics and the locality of Nature. We then suggest a reinterpretation of the EPR experiment that utilizes observer complementarity; a concept from quantum gravity which allows spatially separated observers to have their own, independent reference frames. The resulting picture provides a self-consistent resolution of the situation that does not jeopardize causality nor unitarity, nor …
Bell showed 50 years ago that quantum theory is nonlocal via his celebrated inequalities, turning the issue of quantum nonlocality from a matter of taste into a matter of test. Years later, Hardy proposed a test for nonlocality without inequality, which is a kind of "something-versus-nothing" argument. Hardy's test for $n$ particles induces an $n$-partite Bell's inequality with two dichotomic local measurements for each observer, which has been shown to be violated by all entangled pure states. Our first result is to show that the Bell-Hardy inequality arising form Hardy's nonlocality test is …
Geometric Structure of Bell Correlations in Bohmian Mechanics: A Configuration-Space Analysis of EPR Experiments
本文基于玻姆理论，通过配置空间框架研究EPR-贝尔实验，揭示了测量结果的确定性映射及领域划分，展示贝尔关联源于几何结构，实现无信号性。
Certain predictions of quantum theory are not compatible with the notion of local-realism. This was the content of Bell's famous theorem of the year 1964. Bell proved this with the help of an inequality, famously known as Bell's inequality. The alternative proofs of Bell's theorem without using Bell's inequality are known as `nonlocality without inequality (NLWI)' proofs. We, review one such proof, namely the Hardy's proof which due to its simplicity and generality has been considered the best version of Bell's theorem.
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 study the Bell inequality in a holographic model of the casually disconnected Einstein-Podolsky-Rosen (EPR) pair. The Clauser-Horne-Shimony-Holt(CHSH) form of Bell inequality is constructed using holographic Schwinger-Keldysh (SK) correlators. We show that the manifestation of quantum correlation in Bell inequality can be holographically reproduced from the classical fluctuations of dual accelerating string in the bulk gravity. The violation of this holographic Bell inequality supports the essential quantum property of this holographic model of an EPR pair.
In a recent work [Phys. Rev. Lett. {\bf 98}, 140402 (2007)] we defined ``steering'', a type of quantum nonlocality that is logically distinct from both nonseparability and Bell-nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob's state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state, under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonst…
We have experimentally tested the non local properties of the states generated by a high brilliance source of entanglement which virtually allows the direct measurement of the full set of photon pairs created by the basic QED process implied by the parametric quantum scattering. Standard Bell measurements and Bell's inequality violation test have been realized over the entire cone of emission of the degenerate pairs. By the same source we have verified the Hardy's ladder theory up to the 20th step and the contradiction between the standard quantum theory and the local realism has been tested f…
An explicit model-example is presented to simulate Einstein-Podolsky-Rosen (EPR) experiments without invoking instantaneous influences at a distance. The model-example, together with the interpretation of past experiments by Kwiat and coworkers, uncovers logical inconsistencies in the application of Bell's theorem to actual EPR experiments. The inconsistencies originate from topological-combinatorial assumptions that are both necessary and sufficient to derive all Bell-type inequalities including those of Wigner-d'Espagnat and Clauser-Horne-Shimony-Holt. The model-example circumvents these inc…
Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam …
In a previous paper tests for entanglement for two mode systems involving identical massive bosons were obtained. In the present paper we consider sufficiency tests for EPR steering in such systems. We find that spin squeezing in any spin component, a Bloch vector test, the Hillery-Zubairy planar spin variance test and squeezing in two mode quadratures all show that the quantum state is EPR steerable. We also find a generalisation of the Hillery-Zubairy planar spin variance test for EPR steering. The relation to previous correlation tests is discussed. This paper is based on a detailed classif…
Local realism has been knocked down by the experiments with entangled pairs of particles based on Bell's theorem(J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964)). However, there has been continuing debate on whether locality or realism is the problem. In this work, we analyzed the Einstein-Podolsky-Rosen thought experiment of Bohm's version using information theory and thermodynamics. The inference of non-locality from EPR experiments will be against the principle of non-realism of quantum mechanics. Therefore, the experiments about quantum entanglement cannot provide any proof to a…
We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the framework of relativistic quantum theory to analyze a situation in which measurements are performed by moving observers. We point out that under certain conditions the perfect anti-correlation of an EPR pair of spins in the same direction is deteriorated in the moving observers' frame due to the Wigner rotation, and show that the degree of the violation of Bell's inequality prima facie decreases with increasing the velocity of the observers if the directions of the measurement are fixed. However, this does not imply a…
We develop criteria to detect three classes of nonlocality that have been shown by Wiseman et al. [Phys. Rev. Lett. 98, 140402 (2007)] to be nonequivalent: entanglement, EPR steering, and the failure of local hidden-variable theories. We use the approach of Cavalcanti et al. [Phys. Rev. Lett. 99, 210405 (2007)] for continuous variables to develop the nonlocality criteria for arbitrary spin observables defined on a discrete Hilbert space. The criteria thus apply to multisite qudits, i.e., systems of fixed dimension d, and take the form of inequalities. We find that the spin moment inequalities …
An error in the proof of Bell's Theorem is identified and a semiclassical model of the EPRB experiment is presented
Einstein-Podolsky-Rosen (EPR) steering is an intermediate type of quantum nonlocality which sits between entanglement and Bell nonlocality. A set of correlations is Bell nonlocal if it does not admit a local hidden variable (LHV) model, while it is EPR nonlocal if it does not admit a local hidden variable-local hidden state (LHV-LHS) model. It is interesting to know what states can generate EPR-nonlocal correlations in the simplest nontrivial scenario, that is, two projective measurements for each party sharing a two-qubit state. Here we show that a two-qubit state can generate EPR-nonlocal fu…
The De Broglie-Bohm (DeBB)\cite{DeBB} Causal Quantum Mechanics played a crucial role in Bell's discovery \cite{Bell1964} that quantum mechanics violates EPR local reality \cite{EPR1935}, and also in Bell's search for an exact quantum mechanics. The experiments of Aspect et al \cite{Aspect1981} confirm quantum correlations between plane polarizations of two photons and violation of Bell's inequalities by a factor $\sqrt 2 $. I prove that similar experiments with elliptic polarizers can also show quantum violations of Bell's inequality by the same factor. I summarize our construction of a maxima…
The probabilistic structure of quantum mechanics is investigated in the frequency framework. Such an approach can be interpreted as a contextual approach to quantum probabilities. By using rather complicated frequency calculations we reproduce the EPR-Bohm correlation function which is typically derived by using the calculus of probabilities in a Hilbert space. Our frequency probabilistic model of the EPR-Bohm experiment is a realist model -- physical observables are considered as objective properties of physical systems. It is also local -- a measurement over one part of a composite system do…
A model for two entangled systems in an EPR setting is shown to reproduce the quantum-mechanical outcomes and expectation values. Each system is represented by a small sphere containing a point-like particle embedded in a field. A quantum state appears as an equivalence class of several possible particle-field configurations. Contrarily to Bell-type hidden variables models, the fields account for the non-commutative aspects of the measurements and deny the simultaneous reality of incompatible physical quantities, thereby allowing to escape EPR's "completeness or locality" dilemma.
A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for measurements with continuous variable outcomes is presented to establish criteria for the demonstration of the EPR paradox, for situations where the correlation between spatially separated subsystems is not perfect. Two types of criteria for EPR correlations are determined. The first type are based on measurements of the variances of conditional probability distributions and are necessary to reflect directly the situation of the original EPR paradox. The second weaker set of EPR criteria are based on the proven failure of …
Nowadays, it is commonly admitted that the experimental violation of Bell's inequalities that was successfully demonstrated in the last decades by many experimenters, are indeed the ultimate proof of quantum physics and of its ability to describe the whole microscopic world and beyond. But the historical and scientific story may not be envisioned so clearly: it starts with the original paper of Einstein, Podolsky and Rosen (EPR) aiming at demonstrating that the formalism of quantum theory is incomplete. It then goes through the works of D. Bohm, to finally proceed to the famous John Bell's rel…
Non-locality without inequality is an elegant argument introduced by L. Hardy for two qubit systems, and later generalised to $n$ qubits, to establish contradiction of quantum theory with local realism. Interestingly, for $n=2$ this argument is actually a corollary of Bell-type inequalities, viz. the CH-Hardy inequality involving Bell correlations, but for $n$ greater than 2 it involves $n$-particle probabilities more general than Bell-correlations. In this paper, we first derive a chain of completely new local realistic inequalities involving joint probabilities for $n$ qubits, and then, asso…
A suitable generalized measurement described by a 4-element positive operator-valued measure (POVM) on each particle of a two-qubit system in the singlet state is, from the point of view of Einstein, Podolsky, and Rosen's (EPR's) criterion of elements of reality, equivalent to a random selection between two alternative projective measurements. It is shown that an EPR-experiment with a fixed POVM on each particle provides a violation of Bell's inequality without requiring local observers to choose between the alternatives. This approach could be useful for designing a loophole-free test of Bell…
An elementary topological error in Bell's representation of the EPR elements of reality is identified. Once recognized, it leads to a topologically correct local-realistic framework that provides exact, deterministic, and local underpinning of at least the Bell, GHZ-3, GHZ-4, and Hardy states. The correlations exhibited by these states are shown to be exactly the classical correlations among the points of a 3 or 7-sphere, both of which are closed under multiplication, and hence preserve the locality condition of Bell. The alleged non-localities of these states are thus shown to result from mis…
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