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Richard D. Gill
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I point out critical errors in the paper Bells Theorem Versus Local Realism in a Quaternionic Model of Physical Space by J. Christian, published in IEEE Access. Christians paper in fact contains several conflicting models. None of them form counterexamples to Bells theorem. Most of Christians paper is devoted to a model based on the detection loophole due to Pearle (1970).
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We investigate the nonlocal property of the fractional statistics in Kitaevs toric code model. To this end, we construct the Greenberger-Horne-Zeilinger paradox which builds a direct conflict between the statistics and local realism. It turns out that the fractional statistics in the model is purely a quantum effect and independent of any classical theory.We also discuss a feasible experimental scheme using anyonic interferometry to test this contradiction.
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(A) Bells theorem rests on a conjunction of three assumptions: realism, locality and ``free will. A discussion of these assumptions will be presented. It will be also shown that, if one adds to the assumptions the principle or rotational symmetry of physical laws, a stronger version of the theorem emerges. (B) A link between Bells theorem and communication complexity problems will be presented. This also includes experimental realizations, which surprisingly do not involve entanglement. (C) A new sufficient and necessary criterion for entanglement of general (mixed) states is be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EIs) emerging via this method contains entanglement witnesses (EWs), but they form only a subset of all EIs. Thus the method is more powerful than the one based on EWs.
Bells theorem is a fundamental theorem in physics concerning the incompatibility between some correlations predicted by quantum theory and a large class of physical theories. In this paper, we introduce the hypothesis of accountability, which demands that it is possible to explain the correlations of the data collected in many runs of a Bell experiment in terms of what happens in each single run. Under this assumption, and making use of a recent result by Colbeck and Renner [Nat. Commun. 2, 411 (2011)], we then show that any nontrivial account of these correlations in the form of an extension of quantum theory must violate parameter independence. Moreover, we analyze the violation of outcome independence of quantum mechanics and show that it is also a manifestation of nonlocality.
We introduce a new interpretation of quantum mechanics by examining the Einstein, Podolsky and Rosens (EPR) paradox and Bells inequality experiments under the assumption that the vacuum has an inhomogeneous texture for energy levels below the Heisenberg time-energy uncertainty relation. In this article, selected results from the most reliable Bells inequality experiments will be quantitatively analyzed to show that our interpretation of quantum mechanics creates a new loophole in Bells inequality, and that the past experimental findings do not contradict our new interpretation. Under the vacuum texture interpretation of quantum mechanics in a Bells inequality experiment, the states of the pair of particles created at the source (e.g. during parametric down conversion) is influenced by an inhomogeneous vacuum texture sent from the measurement apparatus. We will also show that the resulting pair of particles are not entangled and that the theory of vacuum texture preserves local realism with complete causality. This article will also suggest an experiment to definitively confirm the existence of vacuum texture.
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