There are two known ways around J.S Bell's famous Inequalities. One is to deny Reichenbach's Common Cause Principle (Bell himself understood this). Another is to impose the lone spin average constraint (Samuel Hedemann discussed this in an obscure preprint). In both cases the Bell Inequality and all generalizations thereof (CHSH, CGLMP and others) cannot be derived, which implies the quantum mechanics correlations one presumes for EPR experiments, and observes, are not necessarily indications of Non-Locality (NL) or anti-Realism (AR). Nevertheless, the orthodox consensus is that our universe is still highly non-classical and EPR-like entanglement correlations are at the heart of the behaviour of non-classical elementary systems. This demands, but we can say "invites," a better account of the observed highly non-classical behaviour of entangled systems, which: (1) respects the (very respectable) lone spin average constraint, and (2) mildly disrespects Reichenbach's principle (RCC), and then (3) explains why one can take the view that either Determinism (D) or (RCC) is violated in quantum processes. We provide a preliminary such account using the principles of topological 4-geon theory (T4G) which leans towards only abandoning the weakest version of (D) possible (deterministic time-evolution) but for very good reason. NB: we have no plans to submit this to a peer review journal, but collaborators with journal access are welcome to inquire about contributing to this preprint to further a peer review process.
There are two known ways around J.S Bell's famous Inequalities. One is to deny Reichenbach's Common Cause Principle (Bell himself understood this). Another is to impose the lone spin average constraint (Samuel Hedemann discussed this in an obscure preprint). In both cases the Bell Inequality and all generalizations thereof (CHSH, CGLMP and others) cannot be derived, which implies the quantum mechanics correlations one presumes for EPR experiments, and observes, are not necessarily indications of Non-Locality (NL) or anti-Realism (AR). Nevertheless, the orthodox consensus is that our universe is still highly non-classical and EPR-like entanglement correlations are at the heart of the behaviour of non-classical elementary systems. This demands, but we can say "invites," a better account of the observed highly non-classical behaviour of entangled systems, which: (1) respects the (very respectable) lone spin average constraint, and (2) mildly disrespects Reichenbach's principle (RCC), and then (3) explains why one can take the view that either Determinism (D) or (RCC) is violated in quantum processes. We provide a preliminary such account using the principles of topological 4-geon theory (T4G) which leans towards only abandoning the weakest version of (D) possible (deterministic time-evolution) but for very good reason. NB: we have no plans to submit this to a peer review journal, but collaborators with journal access are welcome to inquire about contributing to this preprint to further a peer review process.
New types of Bell inequalities and new versions of the Bell theorem will be presented here. They lead to stronger constraints for local realistic theories than the standard inequalities. It will be shown that the fact that such inequalities can be violated indicates not only that we have to abandon classical concepts, but is also a direct indication that quantum states which lead to such violations can, without any further processing, like distillation, etc., be applied to perform tasks with efficiency unattainable for classical systems. Misinterpretations of Bell theorem will be discussed. On one hand, the root of some erroneous claims that there exists a local realistic model for EPR-Bell correlations will be exposed. On the other hand, over-interpretations using vague terms like quantum non-locality or just non-locality will be criticized.
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.
Einstein-Podolsky-Rosen (EPR) correlations Explaining the correlations predicted by quantum mechanics in the case of joint quantum systems of the EPR type has proved to be a major challenge for the Common Cause Principle. The EPR correlations have been confirmed by a large number of sophisticated experiments carried out since the early 1980s, and, since quantum theory does not give us any hints as to where to look for possible common causes that could explain the correlations in question, the suspicion arose that common causes of EPR correlations might not exist at all. If this were indeed the case, then the EPR correlations would constitute strong empirical evidence against Reichenbach's Common Cause Principle. But how could this be possible in view of the results presented in the previous chapters? As we have seen (Chapter 3), every common cause incomplete probability space is common cause extendible (even strongly common cause extendible with respect to any finite set of correlations; Proposition 3.9); therefore every correlation can, in principle, be explained by a (possibly hidden) common cause, including the (finite number of) EPR correlations. Could the EPR correlations (not) be explained by referring to such hidden common causes? To answer this question, one has to realize first that it is not quite obvious how to link the Common Cause Principle to quantum mechanics because Reichenbach's notion of common cause was defined in terms of classical probability theory (Chapter 2), not in terms of quantum probability theory.
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.
Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Starting from the late 60's many experiments have been performed to verify the violation Bell's inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell's inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell's inequality.