Bell's Inequalities — Foundations and Quantum Communication

International Journal of Quantum Information, 2016

In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality. He also showed that QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review...

Quantum [Un]Speakables II

Non-locality, or quantum-non-locality, are buzzwords in the community of quantum foundation and information scientists, which purportedly describe the implications of Bell's theorem. When such phrases are treated seriously, that is it is claimed that Bell's theorem reveals non-locality as an inherent trait of the quantum description of the micro-world, this leads to logical contradictions, which will be discussed here. In fact, Bell's theorem, understood as violation of Bell inequalities by quantum predictions, is consistent with Bohr's notion of complementarity. Thus, if it points to anything, then it is rather the significance of the principle of Bohr, but even this is not a clear implication. Non-locality is a necessary consequence of Bell's theorem only if we reject complementarity by adopting some form of realism, be it additional hidden variables, additional hidden causes, etc., or counterfactual definiteness. The essay contains two largely independent parts. The first one is addressed to any reader interested in the topic. The second, discussing the notion of local causality, is addressed to people working in the field.

2001

The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and empiricist interpretations of the mathematical formalism of quantum mechanics, iii) the distinction between measurement and preparation. It will be demonstrated that an interpretation of violation of Bell's inequality by quantum mechanics as evidence of non-locality of the quantum world is a consequence of a particular choice between these alternatives. Also a distinction must be drawn between two forms of realism, viz. a) realist interpretations of quantum mechanics, b) the possibility of hidden-variables (sub-quantum) theories.

New Journal of Physics, 2006

Bell theorems show how to experimentally falsify local realism. Conclusive falsification is highly desirable as it would provide support for the most profoundly counterintuitive feature of quantum theory-nonlocality. Despite the preponderance of evidence for quantum mechanics, practical limits on detector efficiency and the difficulty of coordinating space-like separated measurements have provided loopholes for a classical worldview; these loopholes have never been simultaneously closed. A number of new experiments have recently been proposed to close both loopholes at once. We show some of these novel designs fail in the most basic way, by not ruling out local hidden variable models, and we provide an explicit classical model to demonstrate this. They share a common flaw, which reveals a basic misunderstanding of how nonlocality proofs work. Given the time and resources now being devoted to such experiments, theoretical clarity is essential. Our explanation is presented in terms of simple logic and should serve to correct misconceptions and avoid future mistakes. We also show a nonlocality proof involving four participants which has interesting theoretical properties.

Bell's theorem: A Faulty Logical Construct, 2025

It is proven that, several implicit assumptions used in the derivation of Bell's inequalities are making them universally valid and therefore, unsuitable either as a criterion for deciding between local realism and quantum mechanics, or as a tool that can be used to prove the existence of entanglement. It is further shown that Bell's theorem can be established only by asserting that the existence of an objective reality implies the exclusion of time from measurements and their outcomes. This exclusion of time is, however, in direct contradiction to the experimental results.

[Abstract]: The mistake of using Bell's Inequality in defeating Hidden Variables as a reasonable solution of EPR Paradox is revealed and discussed. Both entangled photon and electron pairs can change their quantum energy states (hidden variables) through a transformation process (polarization or spin measurement) to a new corresponding entangled quantum state no matter of Bell's Inequality. Because of the existence of predetermined quantum energy states, Schrödinger's Cat and Superposition Theory cannot be true. In addition, the phase angle of a particle wave can be changed by a detector which results in the destruction of interference patterns in Double Slit Interference Experiment, therefore, Complementarity Principle is not true neither.

AIP Conference Proceedings, 2009

A) Bell's 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 Bell's 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 will be presented. It is derived using the same geometric starting point as the inclusion of the symmetry in (A). The set of entanglement identifiers (EI's) emerging via this method contains entanglement witnesses (EW's), but they form only a subset of all EI's. Thus the method is more powerful than the one based on EW's.

Foundations of Physics, 2014

In this paper we give additional arguments in favor of the point of view that the violation of Bell, CHSH and CH inequalities is not due to a mysterious non locality of Nature. We concentrate on an intimate relation between a protocol of a random experiment and a probabilistic model which is used to describe it. We discuss in a simple way differences between attributive joint probability distributions and generalized joint probability distributions of outcomes from distant experiments which depend on how the pairing of these outcomes is defined. We analyze in detail experimental protocols implied by local realistic and stochastic hidden variable models and show that they are incompatible with the protocols used in spin polarization correlation experiments (SPCE). We discuss also the meaning of "free will", differences between quantum and classical filters, contextuality of Kolmogorov models, contextuality of quantum theory (QT) and show how this contextuality has to be taken into account in probabilistic models trying to explain in an intuitive way the predictions of QT. The long range imperfect correlations between the clicks of distant detectors can be explained by partially preserved correlations between the signals created by a source. These correlations can only be preserved if the clicks are produced in a local and deterministic way depending on intrinsic parameters describing signals and measuring devices in the moment of the measurement. If an act of a measurement was irreducibly random they would be destroyed. It seems to indicate that QT may be in fact emerging from some underlying more detailed theory of physical phenomena. If this was a case then there is a chance to find in time series of experimental data some fine structures not predicted by QT. This would be a major discovery because it would not only prove that QT does not provide a complete description of individual physical systems but it would prove that it is not predictably complete.

Alhun Aydın, 2011

Although standard quantum mechanics is compatible with experiments, it could not clarify some important unsolved problems like quantum reality and measurement process. Hidden variable theories provide solutions to these conceptual problems of standard quantum mechanics. We examine Bell's theorem, one of the most essential theorems about foundations of quantum mechanics, and Bell-test experiments which empirically rules out local hidden variable theories. Then we discuss pilot wave theory which is a non-local hidden variable theory and one of the most significant possible successors of standard quantum mechanics. Moreover, by touching upon also philosophical issues, we give the shape of the possible interpretation of quantum mechanics.

SSRN Electronic Journal, 2021

In this article give a very simple presentation of Bell's inequality by comparing it to a "quantum game show", followed by a simple description of Aspect's 1985 experiment involving entangled photons which confirms the inequality. The entire article is non-technical and requires no mathematical background other than high school mathematics and an understanding of basic concepts in probability. The physics involved in Aspect's experiment is also explained.