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In this paper the mystery of local hidden variable theory of quantum mechanics that violates Bell’s inequality is proposed. These ‘hidden variables’ are fundamentally inaccessible to physical experiments. It is not something physicists ever dreamed of. &nbsp

Quantum non-locality tests have been of interest since the 1960s paper by Bell on the original EPR paradox. The present paper discusses whether the CGLMP (Bell) inequalities obtained by Collins et al. are possible tests for showing that quantum theory is not underpinned by local hidden variable theory (LHVT). It is found by applying Fine’s theorem that the CGLMP approach involves a LHVT for the joint probabilities associated with the measurement of one observable from each of the two sub-systems, even though the underlying probabilities for joint measurements of all four observables involve a hidden variable theory which is not required to be local. The latter HVT probabilities involve outcomes of simultaneous measurements of pairs of observables corresponding to non-commuting quantum operators, which is allowed in classical theory. Although the CGLMP inequalities involve probabilities for measurements of one observable per sub-system and are compatible with the Heisenberg uncertainty principle, there is no unambiguous quantum measurement process linked to the probabilities in the CGLMP inequalities. Quantum measurements corresponding to the different classical measurements that give the same CGLMP probability are found to yield different CGLMP probabilities. However, violation of a CGLMP inequality based on any one of the possible quantum measurement sequences is sufficient to show that the Collins et al. LHVT does not predict the same results as quantum theory. This is found to occur for a state considered in their paper—though for observables whose physical interpretation is unclear. In spite of the problems of comparing the HVT inequalities with quantum expressions, it is concluded that in spite of the contextuality loophole, the CGLMP inequalities are indeed suitable for ruling out local hidden variable theories and also non-local ones as well. The state involved could apply to a macroscopic system, so the CGLMP Bell inequalities are important for finding cases of macroscopic violations of Bell locality. Possible experiments in double-well Bose condensates involving atoms with two hyperfine components are discussed.

In 1948, Schwinger developed a local Lorentz covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger's theory is presented, which makes all of the same empirical predictions as conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant 'local hidden variable theory' in space-time, whose existence proves definitively that such theories are possible. There is no inconsistency with Bell's theorem because this a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems' wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given., Comment: 22 pages, 6 figures

Entanglement, according to Erwin Schrodinger the essence of quantum mechanics, is at the heart of the Einstein-Podolsky-Rosen paradox and of the so-called “quantum nonlocality"—the fact that a local realistic explanation of quantum mechanics is not possible as quantitatively expressed by violation of Bell’s inequalities. Even as entanglement gains increasing importance in most quantum information processing protocols, its conceptual foundation is still widely debated. Among the open questions are: What is the conceptual meaning of quantum entanglement? What are the most general constraints imposed by local realism? Which general quantum states violate these constraints? Developing Schrodinger’s ideas in an information-theoretic context, we suggest that a natural understanding of quantum entanglement results when one accepts (1) that the amount of information per elementary system is finite and (2) that the information in a composite system resides more in the correlations than in properties of individuals. The quantitative formulation of these ideas leads to a rather natural criterion of quantum entanglement for pure states, which starts from the amount of information in correlations, rather than the non-factorizability of Hilbert space vectors representing the states. Independently, extending Bell’s original ideas, one can obtain a single general Bell inequality that summarizes all possible constraints imposed by local realism on the correlations for a multi-qubit system, and for situations in which the observers can choose between two (complementary) measurements. Violation of the general Bell inequality results in an independent general criterion for quantum entanglement for multi-qubit states. Most importantly, the two criteria agree in essence, though the two approaches are conceptually very different. This concurrence supports our information-theoretic interpretation of quantum entanglement| and of quantum physics in general.

We review classical properties of harmonic-oscillator coherent states. Then we discuss which of these classical properties are preserved under the group-theoretic generalization of coherent states. We prove that the generalized coherent states of quantum systems with Lie-group symmetries are the unique Bell states, i.e., the pure quantum states preserving the fundamental classical property of satisfying Bell’s inequality upon splitting.

The violation of the Bell inequalities implies that quantum mechanics cannot be interpreted using any local hidden variable theory. However, particular quantum states that can originally be described using a local hidden variable model surprisingly exhibit nonlocality by employing local filters before a standard Bell test is performed. This is referred to as hidden nonlocality. In this study, we provide the experimental demonstration of hidden nonlocality through linear optics towards the local states which are put forword by Hirsch et al., PRL 111, 160402 (2013). A class of local states is generated through a spontaneous parametric down-conversion process, and the violation of the Clauser–Horne–Shimony–Holt (CHSH)–Bell inequality is observed by applying local filters. Our experimental results confirm the superiority of local filters, and throw light on deep understanding the intriguing phenomena of hidden nonlocality and local states.

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 Einstein-Podolsky-Rosen (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 generalization 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 classification of quantum states for bipartite systems. States for bipartite composite systems are categorized in quantum theory as either separable or entangled, but the states can also be divided differently into Bell local or Bell nonlocal states in terms of local hidden variable theory (LHVT). For the Bell local states there are three cases depending on whether both, one of or neither of the LHVT probabilities for each subsystem are also given by a quantum probability involving subsystem density operators. Cases where one or both are given by a quantum probability are known as local hidden states (LHSs) and such states are nonsteerable. The steerable states are the Bell local states where there is no LHS, or the Bell nonlocal states. The relationship between the quantum and hidden variable theory classification of states is discussed.

In this article we show that results similar to those of the Einstein-Podolsky-Rosen-Bohm (EPRB) Gedankenexperiment and entanglement of photons can be obtained using weak classical light waves if we take into account the discrete (atomic) structure of the detectors and a specific nature of the light-atom interaction. We show that the CHSH (Clauser, Horne, Shimony, and Holt) criterion in the EPRB Gedankenexperiment with classical light waves can exceed not only the maximum value S HV =2 that is predicted by the local hidden-variable theories but also the maximum value S Q M = 2 2 \({S_{QM}} = 2\sqrt 2 \) predicted by quantum mechanics.

The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell’s theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.

A discussion of Nieuwenhuizen’s description for the hidden variables of the detectors in the derivation of Bell’s theorem is presented. This description prevents Bell’s inequalities from being effected. However it will be argued, on mathematical and physical bases, that the flaws attributed by Nieuwenhuizen to Bell’s probability distribution function are unjustified.

It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.

A detailed explication of Edwin Jaynes’ criticism of Bell’s deviation of his renowned inequality is presented. The exact consequence of an incorrect symbolic rendition for a conditional probability for the derivation is illustrated. Additionally, a data-point by data-point simulation of an optical test intended to exploit a Bell Inequality for demonstrating the inevitability of either irreality or nonlocality is described. This simulation shows in detail that only non correlated signal pairs do not violate the chosen form of a Bell Inequality, contrary to the intended hypothetical input into Bell’s derivation. Finally, attention is drawn to the fact that, von Neumann’s “Projection Hypothesis” is the basic conception behind nonlocality in quantum theory.

Violation of Mermin's and Svetlichny's inequalities can rule out the predictions of local hidden variable theory and can confirm the existence of true nonlocal correlation for n-particle pure quantum systems. Here we demonstrate the experimental violation of the above inequalities for W- and GHZ-class of states. We use IBM's five-qubit quantum computer for experimental implementation of these states and illustration of inequalities' violations. Our results clearly show the violations of both Mermin's and Svetlichny's inequalities for W and GHZ states respectively. Being a superconducting qubit-based quantum computer, the platform used here opens up the opportunity to explore multipartite inequalities which is beyond the reach of other existing technologies., Comment: 5 pages, Comments are welcome!

The categorization of quantum states for composite systems as either separable or entangled, or alternatively as Bell local or Bell non-local states based on local hidden variable theory is reviewed in Sections 1 and 2, focusing on simple bipartite systems. The significance of states demonstrating Bell non-locality for settling the long standing controversy between the Copenhagen interpretation of the quantum measurement process involving the collapse of the wave-function and the alternative interpretation based on pre-existing hidden variables is emphasized. Although experiments demonstrating violations of Bell locality in microscopic systems have now been carried out (see Section 3), there is current interest in finding Bell non-locality in quantum systems on a macroscopic scale, since this is a regime where a classical hidden variable theory might still apply. Progress towards finding macroscopic quantum states that violate Bell inequalities is reviewed in Section 4. A new test for Bell non-locality that applies when the sub-system measured quantities are spin components with large outcomes is described, and applied to four mode systems of identical massive bosons in Bose-Einstein condensates., 18 pages, 1 figure. Version 2 unchanged except figure now visible

Bell’s theorem is sometimes taken to show that quantum mechanics undermines scientific realism. If so, this would be a striking empirical argument against realism. However, Maudlin has claimed that this is a mistake, since Bell’s theorem has precisely one conclusion—namely that quantum mechanics is non-local. I argue here that matters are more complicated than Maudlin acknowledges: quantum mechanics is not a unified theory, and what Bell’s theorem shows of it depends on which interpretation turns out to be tenable. I conclude that while the lesson of Bell’s theorem could be that quantum mechanics is non-local, it could equally be that measurements have multiple outcomes, or that effects can come before their causes, or even, as the anti-realist contends, that no description of the quantum world can be given.

Quantum entanglement is widely believed to be a feature of physical reality with undoubted (though debated) metaphysical implications. But Schrodinger introduced entanglement as a theoretical relation between representatives of the quantum states of two systems. Entanglement represents a physical relation only if quantum states are elements of physical reality. So arguments for metaphysical holism or nonseparability from entanglement rest on a questionable view of quantum theory. Assignment of entangled quantum states predicts experimentally confirmed violation of Bell inequalities. Can one use these experimental results to argue directly for metaphysical conclusions? No. Quantum theory itself gives us our best explanation of violations of Bell inequalities, with no superluminal causal influences and no metaphysical holism or nonseparability—but only if quantum states are understood as objective and relational, though prescriptive rather than ontic. Correct quantum state assignments are backed by true physical magnitude claims: but backing is not grounding. Quantum theory supports no general metaphysical holism or nonseparability; though a claim about a compound physical system may be significant and true while similar claims about its components are neither. Entanglement may well have have few, if any, first-order metaphysical implications. But the quantum theory of entanglement has much to teach the metaphysician about the roles of chance, causation, modality and explanation in the epistemic and practical concerns of a physically situated agent.

We present an option of the experiment with a correlated pair of particles in the entangled state, which provides the effect of a change in the polarization for entangled photons, and demonstrate the reality of all different superposition states and the corresponding vector of the quantum system state; also we analyze possible consequences of this fact. We propose a quantum realism paradigm within the relational paradigm instead of the local realism concept disproved by the experiments on verifying the Bell inequalities. We analyze the results of experimental research of the Leggett inequality violation with respect to the verification of the adequacy of different kinds of nonlocal hidden variable theories and suggest a new way of their evaluation based on the study of the photon cross-correlation suppression after a beam splitter and preparation of quantum squeezed states. We show that the interpretation based on the nonlocal hidden variable theory is inconsistent.

The number of steps required in order to maximize a Bell inequality for arbitrary number of qubits is shown to grow exponentially with the number of parties involved. The proof that the optimization of such correlation measure is an NP-problem based on an operational perspective involving a Turing machine, which follows a general algorithm. The implications for the computability of the so-called nonlocality for any number of qubits is similar to recent results involving entanglement or similar quantum correlation-based measures.

We propose a formalism to derive the maximal bound of generalized Bell type correlation and shows that the formalism can be applied to various form of Bell functions. The Bell function is defined to generate correlations of multiparty high-dimensional system whose local hidden variable bound can be obtained from the series of the constraint equations. The application of the constraints converts the optimization problem into the counting problems whose complexity is dramatically reduced. It is also shown that the correlation can be used to generate many other known Bell type functions such as Mermin, Ardehali, Svetlichny functions for multipartite two-dimensional class.

We extend the Bell inequality known for two qubits to the four-level atom, including an artificial atom realized by the superconducting circuit, and qudit with j = 3/2. We formulate the extended inequality as the inequality valid for an arbitrary Hermitian nonnegative 4×4 matrix with unit trace for both separable and entangled matrices.

Today, quantum-mechanical concepts i.e. such as non-locality refer to some mathematical foundations, especially to Bell’s inequality and the Chsh inequality. Experimental data, analyzed while using Bell’s inequality or the Chsh inequality, favor a quantum mechanical description of nature over local hidden variable theories (often referred to as local realism). In general, the use of mathematically inconsistent methods can imply a waste of money, time and effort on this account. Under some certain conditions (the assumption of independence) Bell’s theorem and the Chsh inequality are already refuted. The purpose of this publication is to explore the terra incognita, the interior logic that may lie beyond Bell’s original theorem and the Chsh inequality and to refute both Bell’s original theorem and the Chsh inequality under any circumstances by the proof that we can derive a logical contradiction out of Bell’s inequalities. Thus far, if you accept Bell’s theorem or the Chsh inequality as correct, then you must accept too that +0 = +1, which is a logical contradiction. Bell’s theorem and the Chsh inequality are refuted in general. In this insight, it appears to be necessary to revisit the very foundations of quantum theory and of physics as such.

Intrinsic quantum correlations supported by the $SU(2)\otimes SU(2)$ structure of the Dirac equation used to describe particle/antiparticle states, optical ion traps and bilayer graphene are investigated and connected to the description of local properties of Dirac bi-spinors. For quantum states driven by Dirac-like Hamiltonians, quantum entanglement and geometric discord between spin and parity degrees of freedom - sometimes mapped into equivalent low energy internal degrees of freedom - are obtained. Such \textit{spin-parity} quantum correlations and the corresponding nonlocal intrinsic structures of bi-spinor fermionic states can be classified in order to relate quantum observables to the (non)local behavior of these correlations. It is shown that free particle mixed states do not violate the Clauser-Horne-Shymony-Holt inequality: the correlations in such mixed bi-spinors, although quantum, can be reproduced by a suitable local hidden variable model. Additionally, the effects due to a non-minimal coupling to a homogeneous magnetic field, and to the inclusion of thermal effects are evaluated, and quantum correlations of associated quantum mixtures and of the thermal states are all quantified.The above-mentioned correlation quantifiers are then used to measure the influence of CP transformations on \textit{spin-parity} quantum correlations, and our results show that quantum entanglement is invariant under CP transformations, although the geometric discord is highly sensitive to the CP symmetry., 27 pages, 5 figures

Machine learning, the core of artificial intelligence and big data science, is one of today's most rapidly growing interdisciplinary fields. Recently, machine learning tools and techniques have been adopted to tackle intricate quantum many-body problems. In this Letter, we introduce machine learning techniques to the detection of quantum nonlocality in many-body systems, with a focus on the restricted-Boltzmann-machine (RBM) architecture. Using reinforcement learning, we demonstrate that RBM is capable of finding the maximum quantum violations of multipartite Bell inequalities with given measurement settings. Our results build a novel bridge between computer-science-based machine learning and quantum many-body nonlocality, which will benefit future studies in both areas.

Although skeptical of the prohibitive power of no-hidden-variables theorems, John Bell was himself responsible for the two most important ones. I describe some recent versions of the lesser known of the two (familar to experts as the "Kochen-Specker theorem") which have transparently simple proofs. One of the new versions can be converted without additional analysis into a powerful form of the very much better known "Bell's Theorem", thereby clarifying the conceptual link between these two results of Bell., 27 pages, no figures. An initial page explains why I am posting this 25-year-old article

In a recent paper on Foundations of Physics, Stephen Boughn reinforces a view that is more shared in the area of the foundations of quantum mechanics than it would deserve, a view according to which quantum mechanics does not require nonlocality of any kind and the common interpretation of Bell theorem as a nonlocality result is based on a misunderstanding. In the present paper I argue that this view is based on an incorrect reading of the presuppositions of the EPR argument and the Bell theorem and, as a consequence, is unfounded.

We discuss the connection between the incompatibility of quantum measurements, as captured by the notion of joint measurability, and the violation of Bell inequalities. Specifically, we present explicitly a given a set of non jointly measurable POVMs $\mathcal{M}_A$ with the following property. Considering a bipartite Bell test where Alice uses $\mathcal{M}_A$, then for any possible shared entangled state $\rho$ and any set of (possibly infinitely many) POVMs $\mathcal{N}_B$ performed by Bob, the resulting statistics admits a local model, and can thus never violate any Bell inequality. This shows that quantum measurement incompatibility does not imply Bell nonlocality in general., Comment: See also arXiv:1705.10069 for a related work Small changes on the main text. Some typos were fixed

This paper aims to implement Bell’s notion of local causality into a framework, called local physical theory, which is general enough to integrate both probabilistic and spatiotemporal concepts and also classical and quantum theories. Bell’s original idea of local causality will then arise as the classical case of our definition. First, we investigate what is needed for a local physical theory to be locally causal. Then we compare local causality with Reichenbach’s common cause principle and relate both to the Bell inequalities. We find a nice parallelism: both local causality and the common cause principle are more general notions than captured by the Bell inequalities. Namely, Bell inequalities cannot be derived neither from local causality nor from a common cause unless the local physical theory is classical or the common cause is commuting, respectively.

Bell's theorem is one of the most profound scientific discoveries ever made, namely the one which establishes a departure of the nondeterministic quantum mechanical predictions from our local realistic view of the world. In essence, based on Einstein's locality conditions, the theorem settles an experimentally verifiable constraint (Bell's inequality) on the statistical correlations between the observables of spatially separated pairs of entangled particles. Here, based on the notion of sequential weak measurements, we propose a framework to test Bell's inequality in a bipartite system with only local operations made by one of the parties. This novel scenario represents a great simplification of the problem, in the sense that only one of the particles of an entangled pair is required to be manipulated and detected. The importance of the use of pointer states endowed with orbital angular momentum in the present case is also demonstrated .

An earlier article in this journal introduced a renegade theory called the Theory of Elementary Waves (TEW). Whereas quantum mathematics (QM) is a science of observables, TEW is a science of physical nature independent of the observer. They are symmetrical: complement and support each other. That article left three dangling threads that this article addresses: 1. Our claim that TEW is the only local realistic theory that can explain Bell test experiments, 2. Focusing on the medium in which elementary waves move, and 3. Demonstrating that there is zero experimental support wave particle duality. TEW is neither the hidden variable theory of Einstein, Podolsky and Rosen (EPR), nor the absorber theory of Wheeler and Feynman, nor an offshoot nor variant of quantum theory. It is a new paradigm, discovered by a dissident, Lewis E. Little who, after his PhD in physics, worked alone for decades outside the ivory tower of academic physics searching for and eventually finding a theory that explains quantum experiments based on local realism. The fate of new paradigms, unfortunately, is to be rejected as gibberish by leaders of the old paradigm. Plate tectonics was dismissed as absurd during the twentieth century.

In view of the problem that there is only one typical Bell basis for QT (Quantum Teleportation), three new GBBs (Generalized Bell Bases) are obtained by transforming unitarily the Hadamard gates with the methods of Pauli gates in the quantum circuit of the traditional Bell basis, and four Bell bases have an identical general formula. Three controlled-QT schemes are proposed based on these GBBs. The changed processes of quantum entangled states during QT in these schemes are derived by using the similar method of the traditional Bell basis. The result analyses of quantum state collapses of controlled-QT show that more two-qubit quantum entanglement resources of Bell states can be available. These schemes can be considered as the beneficial supplements for current QT work with GBS (Generalized Bell State).

In this paper, using the quantum entanglement swapping technologies under the collective-dephasing noise and the collective-rotation noise, two robust quantum dialogue protocols are proposed, respectively. The logical Bell states are used as the traveling states to combat the collective noise. The auxiliary logical Bell state is shared privately between two participants through the manner of direct transmission first. After encoded with the receiver's secret messages, it swaps entanglement with its adjacent logical Bell state. In this way, the information leakage problem is avoided. Moreover, Eve's active attacks can be detected with the help of decoy photon technology. For decoding, the Bell state measurements rather than the four-qubit joint measurements are needed.

The aim of the paper is to relate Bell’s notion of local causality to the Causal Markov Condition. To this end, first a framework, called local physical theory, will be introduced integrating spatiotemporal and probabilistic entities and the notions of local causality and Markovity will be defined. Then, illustrated in a simple stochastic model, it will be shown how a discrete local physical theory transforms into a Bayesian network and how the Causal Markov Condition arises as a special case of Bell’s local causality and Markovity.

One of the most astonishing features of quantum mechanics is that of the entanglement of particles. First introduced as an objection to quantum mechanics by the famous Einstein, Podolsky and Rosen (EPR) thought experiment, entanglement represents the notion of non-local quantum correlations between two or more quantum-mechanical systems. That is, for an entangled pair of particles the measurement of an observable for one particle immediately determines the corresponding value for the other particle, regardless of the distance between the two particles. This property of entangled systems led to a number of implications that disturbed many scientists and resulted in the emergence of hidden variable theories. Local hidden variable theory assumes that nature can be described by local processes, in which information and correlations propagate at most at the speed of light and in which the observables of a physical system are determined by some unknown (hidden) variables. It was not until the 1960s when Bell's inequality (and Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality) demonstrated the possibility of practical experiments to test the validity of quantum theory with respect to local hidden variable theories. A slew of experiments followed to test Bell's inequality, each of which violated the inequality and in turn verified quantum mechanical predictions of entanglement. These results encouraged the search for a method of producing maximally entangled states. Spontaneous parametric down-conversion (SPDC) has proved to be the most efficient technique in generating two-photon entanglement, in which a single photon is split into a pair of lower frequency photons. Shih and Alley were the first to demonstrate a violation of Bell's inequality using SPDC-generated photon pairs. This demonstration was the start of various polarisation-entanglement experiments; however, in 2001, it was shown that the orbital angular momentum (OAM) of light could also be used as a basis for entanglement. The spatial modes associated with different OAM states also demonstrated a distinct advantage over polarisation with regard to the number of states available. Spatial modes possessing OAM have been studied often in recent years because of the infinite-dimensional alphabets they can possibly provide. In particular, the OAM modes of a photon are a very good avenue for exploring higher dimensions. Quantum mechanics in higher dimensional systems has the potential of revolutionising quantum communication and computation protocols. As an example, quantum cryptography using qudits (systems in which there are d orthogonal states) has been shown to be more secure and robust in the presence of noise. Quantum entanglement has sparked an interest in a number of scientific fields, such as quantum information processing, quantum cryptography and quantum teleportation. In this paper we report on the first entanglement experiment in South Africa, where quantum correlations were observed for the first time in Africa in 2011. We create a bi-photon pair entangled in their spatial modes, allowing quantum states of high dimension. The paper should serve as a useful guide to encourage further quantum experiments in the region.

Entanglement is defined in terms of some kind of instantaneous interaction, contrary to the relativistic principle that all interaction is possible only at a velocity less than that of light. This conflict with an otherwise inviolate principle justifies re-examination of the arguments leading to its (ostensible) rejection. Herein the historically essential notion, namely wave-collapse by measurement or the “Projection Hypothesis” of von Neumann is brought to attention and seen to violate Popper’s Principle of negatability; thereby disqualifying it as a scientific proposition. Further, it is observed that polarization of electromagnetic signals as used in experiments testing Bell Inequalities is described by structure excluding quantum principles. Consequently, most experiments taken to verify Bell’s conclusions cannot in principle do so: a quantum effect cannot be found where there is no quantum structure. Finally, a simple simulation which demonstrates the classical (electromagnetic) generation of the data that violates a Bell Inequality, thereby proving by counterexample that Bell’s so-called theorem is misunderstood, is presented.

Quantum Mechanics formalism remains difficult to understand and sometimes is confusing, especially in the explanation of ERP paradox and of Bell’s inequalities with entanglement photons. So a chart of conversion, in which elements are named differently, is proposed. Next, experiment about Bell’s inequalities violation is described in another way, and we hope a clearer one. Main result is Bell’s inequalities would not be violated! The explanation would come from confusion between the definition of the correlation function S1, and a property S2. And consequently, Einstein, Podolski and Rosen would be right on the local “hidden” variable.

Quantum mechanics is a probabilistic theory of the universe suggestive of a mean value theory similar to thermodynamics prior to the introduction of the atomic theory. If QM will follow a similar path to thermodynamics, then a local deterministic theory must be developed which matches QM predictions. There have been four tough barriers to a local theory of light, of which Bell’s Theorem has been considered the ultimate barrier. The other three barriers are explaining spontaneous emission, the reflection of a small fraction of light at a dielectric interface and the splitting action of a polarizer on polarized light (Malus’ Law). The challenge is that in a local theory of light, everything must have a specific cause and effect. There can be nothing spontaneous or hidden. Local solutions to all four of these barriers are presented in this paper, integrating results from two previous papers and adding the solution paths to the third and fourth barriers as well, which are nearly identical. A previous paper [1] used results from Einstein’s famous 1917 paper on stimulated emission to provide a deterministic local model for spontaneous emission. A second paper [2] showed that QM predictions in tests of Bell’s theorem could be matched with a local model by modifying the definition of entanglement in a manner invisible to quantum mechanics. This paper summarizes and extends those two results and then presents a deterministic model of reflection from a dielectric interface and transmission of polarized light through a polarizer that both match quantum mechanics. As the framework of a local theory of light emerges, it is not surprising that we find corners of physics where small disagreements with quantum mechanics are predicted. A new Bell type test is described in this paper which can distinguish the local from the nonlocal theory, giving predictions that must disagree slightly but significantly with quantum mechanics. If such experiments are proven to disagree with quantum mechanics, then the door to a local theory of light will be opened.

We study the relation between hidden variables theories and quantum computation. We discuss an inconsistency between a hidden variables theory and controllability of quantum computation. To derive the inconsistency, we use the maximum value of the square of an expected value. We propose a solution of the problem by using new hidden variables theory. Also we discuss an inconsistency between hidden variables theories and the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be an easy detector to Pauli observable. We cannot accept hidden variables theories to simulate the double-slit experiment in a specific case. Hidden variables theories may not depicture quantum detector. This is a quantum measurement theoretical profound problem.

Until now, the quintessential demonstration of quantum entanglement has required extra assumptions.

Chapters 1– 12 form what could be the basis for a one semester course in quantum mechanics. Before moving on to advanced topics such as time-independent perturbation theory, the variational method, the WKB approximation and irreducible tensor operators, it can’t hurt to review the basic concepts of quantum mechanics that I have covered up to this point. I also use this chapter to discuss an alternative formulation of quantum mechanics given by Feynman based on path-integrals. Finally I present a proof of Bell’s theorem and see how it can be tested.

It was first observed by John Bell that quantum theory predicts correlations between measurement outcomes that lie beyond the explanatory power of local hidden variable theories. These correlations have traditionally been studied extensively in the probabilistic framework. A drawback of this perspective is that one is then forced to use in a single argument the outcomes of mutually-exclusive measurements. One of us has initiated an alternative approach, invoking only data at hand, in order to circumvent this issue. In this factual view, which is based on Kol-mogorov complexity, we introduce mechanisms such as complexity amplification. We establish that this functionality is realizable, just as its probabilistic counterpart, hereby underlining that Bell correlations are a precious information-processing resource.

Quantum Correlations are studied extensively in quantum information domain. Entanglement Measures and Quantum Discord are good examples of these actively studied correlations. Detection of violation in Bell inequalities is also a widely active area in quantum information theory world. In this work, we revisit the problem of analyzing the behavior of quantum correlations and violation of Bell inequalities in noisy channels. We extend the problem defined in a recent study by observing the changes in negativity measure, quantum discord and a modified version of Horodecki measure for violation of Bell inequalities under amplitude damping, phase damping and depolarizing channels. We report different interesting results for each of these correlations and measures. All these correlations and measures decrease under decoherence channels, but some changes are very dramatical comparing to others. We investigate also separability conditions of example studied states.

Quantum mechanics is known to provide significant improvements in information processing tasks when compared to classical models. These advantages range from computational speeds-up to security improvements. A key question is where these advantages come from. The toy model developed by Spekkens [R. W. Spekkens PRA 75, 032110 (2012)] mimics many of the features of quantum mechanics, such as entanglement and no-cloning, regarded as being important in this regard, despite being a local hidden variable theory. In this work we study several protocols within Spekkens' toy model where we see it can also mimic the advantages and limitations shown in the quantum case. We first provide explicit proofs for the impossibility of toy bit-commitment and the existence of a toy error correction protocol and consequent $k-$threshold secret sharing. Then, defining a toy computational model based on the quantum one-way computer we prove the existence of blind and verified protocols. Importantly, these two last quantum protocols are known to achieve a better-than-classical security. Our results suggest that such quantum improvements need not arise from any Bell-type non locality or contextuality, but rather as a consequence of steering correlations., Comment: 25 pages, 3 figures; Several changes from previous version, overall readability and structure improved. Many notation issues and typos fixed

The recent loophole-free experiments have confirmed the violation of Bell?s inequalities in nature. Yet, in order to insert measured values in Bell?s inequalities, it is unavoidable to make a hypothesis similar to ?ergodicity at the hidden variables level?. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell?s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell?s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment. Fil: Hnilo, Alejandro Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones Científicas y Técnicas para la Defensa. Centro de Investigación en Láseres y Aplicaciones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Unidad de Investigación y Desarrollo Estratégico para la Defensa. Ministerio de Defensa. Unidad de Investigación y Desarrollo Estratégico para la Defensa; Argentina

The violation of Bell's theorem is a very simple way to see that there is no underlying classical interpretation of quantum mechanics. The measurements made on the photons shows that light signal (information) could travel between them, hence completely eliminating any chance that the result was due to anything other than entanglement. Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. It was found that violation of Bell's inequalities could be trivially calculated and for sets of nonmaximally entangled states of two qubits, comparing these entanglement measures may lead to different entanglement orderings of the states. On the other hand, although it is not an entanglement measure and not monotonic under local operations, due to its ability of detecting multipartite entanglement, quantum Fisher information (QFI) has recently received an intense attraction generally with entanglement in the focus. In this work, we visit violation of Bell's inequalities problem with a different approach. Generating a thousand random quantum states and performing an optimization based on local general rotations of each qubit, we calculate the maximal QFI for each state. We analyze the maximized QFI in comparison with violation in Bell's inequalities and we make similar comparison of this violation with commonly studied entanglement measures, negativity and relative entropy of entanglement. We show that there are interesting orderings for system states.

Entanglement in quantum mechanics contradicts local realism and is a manifestation of quantum nonlocality. Its presence can be detected through the violation of Bell, or Clauser-Horne-Shimony-Holt (CHSH) inequalities. Paradigmatic quantum systems provide examples of both, nonentangled and entangled states. Here, we consider a minimal complexity setup consisting of six Majorana zero modes. We find that any allowed state in the degenerate Majorana space is nonlocally entangled. We show how to measure (with available techniques) the CHSH-violating correlations using either intermediate strength or weak measurement protocols.