Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this quantum effect is solely responsible for violation of Bell's Inequalities within this model. The Bell states can be represented by products of these spin states and leads to the intuitive concept that as entangled states decompose they form biparticles that are not entangled. In EPR coincidence experiments filter settings for both the Bell and CHSH forms of Bell's Inequalities are rationalized in terms of the correlation between biparticles.
Violation of Bell's Inequalities gives experimental evidence for the existence of a spin 1/2 which has two simultaneous axes of spin quantization rather than one. These couple to form a resonance state, called the spin fringe, and this quantum effect is solely responsible for violation of Bell's Inequalities within this model. The Bell states can be represented by products of these spin states and leads to the intuitive concept that as entangled states decompose they form biparticles that are not entangled. In EPR coincidence experiments filter settings for both the Bell and CHSH forms of Bell's Inequalities are rationalized in terms of the correlation between biparticles.
Abstract A statistical simulation is presented which reproduces the correlation obtained from EPR coincidence experiments without non-local connectivity. We suggest that spin carries two complementary properties. In addition to the spin polarization, we identify spin coherence. This spin attribute is anti-symmetric and generates the helicity. In addition this spin has structure formed from two orthogonal magnetic moments. From these, a resonance spin results from their coupling in free flight. Upon encountering a filter, the resonance spin 1 decouples back into two independent spins of ½, with one aligning with the filter and the other randomizing. The process of decoupling the resonance spin is responsible for the quantum correlation which results in the observe violation of Bell's Inequalities. The polarized states give a CHSH value of 2 while the resonance spin give a CHSH value of 1. Coherence can only be formulated by the existence of a bivector which gives a spin the same geometric structure as a photon. Although this work is not about Bell's theorem, we note that there are no hidden variables (HV). The only local variable is the angle that orients a spin on the Bloch sphere, first identified in the 1920's. The new features introduced are changing the spin symmetry from SU(2) to the quaternion group, Q8, and the introduction of a bivector into spin which leads to an element of reality which is anti-Hermitian. The calculations use standard spin algebra, and properties of quaternions. March 28, 2023
SANCTUARY, McGill University | The exact violation of Bell’s Inequalities is obtained with a local realistic model for spin. The model treats one particle that comprises a quantum ensemble and simulates the EPR data one coincidence at a time as a product state. Such a spin is represented by operators x;i y; z in its body frame rather than the usual set of X; Y ; Z in the laboratory frame. This model, assumed valid in the absence of a measuring probe, contains both quantum polarizations and coherences. Each carries half the EPR correlation, but only half can be measured using coincidence techniques. The model further predicts the lter
Bell inequalities are intended to formulate mathematically the argument of the thought-experiment proposed by Einstein, Podolsky and Rosen (EPR) in the Einstein-Bohr Debate. Devised to test Bell inequalities against quantum mechanics for resolving the Einstein-Bohr debate, Bell experiments are purportedly modern versions of the EPR experiment. However, there exists a fatal logical flaw in Bell experiments. Because of the logical flaw, Bell experiments differ essentially from the EPR experiment, and quantum correlation in the EPR experiment is not "quantum entanglement" in Bell experiments; the latter is not physically meaningful. In addition to the logical flaw in Bell experiments, a physical constraint imposed on measuring individual quantum objects is violated by all Bell inequalities, which makes Bell inequalities physically meaningless. Unlike Bell experiments, the EPR experiment will not violate any physical constraint, and the EPR argument has no logical flaw. Consequently, the experimental invalidation of Bell inequalities is not evidence for falsifying the two fundamental hypotheses for scientific research, i.e., locality and realism, underlying the EPR experiment, and by no means can Bell experiments resolve the Einstein-Bohr debate. Stemming from abandoning either locality or realism or both, the so-called new applications of quantum mechanics, including various quantum information technologies, are all ineligible and doomed to failure, for they attempt to exploit physically meaningless "quantum superposition" or "quantum entanglement", treating them as physical resources "out there" in the real world.
Bell’s inequalities (BIs) derived in terms of quantum probability statistics are extended to general bipartite-entangled states of arbitrary spins with parallel polarization. The original formula of Bell for the two-spin singlet is slightly modified in the parallel configuration, while the inequality formulated by Clauser–Horne–Shimony–Holt (CHSH) remains unchanged. The violation of BIs indeed resulted from the quantum nonlocal correlation for spin-[Formula: see text] case. However, the inequalities are always satisfied for the spin-1 entangled states regardless of parallel or antiparallel polarizations of two spins. The spin parity effect originally demonstrated with the antiparallel spin-polarizations (Z. Song, J.-Q. Liang and L.-F. Wei, Mod. Phys. Lett. B 28 (2013) 145004) still exists for the parallel case. The quantum nonlocality does not lead to the violation for integer spins due to the cancellation of nonlocal interference effects by the quantum statistical average. Again, the violation of BIs seems to be a result of the measurement-induced nontrivial Berry phase (BP) for half-integer spins.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
The identification and physical interpretation of arbitrary quantum correlations are not always effortless. Two features that can significantly influence the dispersion of the joint observable outcomes in a quantum bipartite system composed of systems I and II are: (a) All possible pairs of observables describing the composite are equally probable upon measurement, and (b) The absence of concurrence (positive reinforcement) between any of the observables within a particular system; implying that their associated operators do not commute. The so-called EPR states are known to observe (a). Here, we demonstrate in very general (but straightforward) terms that they also satisfy condition (b), a relevant technical fact often overlooked. As an illustration, we work out in detail the three-level systems, i.e., qutrits. Furthermore, given the special characteristics of EPR states (such as maximal entanglement, among others), one might intuitively expect the CHSH correlation, computed exclusively for the observables of qubit EPR states, to yield values greater than two, thereby violating Bell's inequality. We show such a prediction does not hold true. In fact, the combined properties of (a) and (b) lead to a more limited range of values for the CHSH measure, not surpassing the nonlocality threshold of two. The present constitutes an instructive example of the subtleties of quantum correlations.