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Local Hidden Variable Theory of Quantum Mechanics that Violates Bell's Inequality

Henok Tadesse

Published Jan 26, 2023• 0 citations
Publisher

Abstract

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.
DOI
10.5281/zenodo.7572273

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The conceptually puzzling features of quantum mechanics as a statistical theory all have their source in the impossibility of relating the probability assignments defined by the quantum state to distributions over determinate values of the physical magnitudes. While some interpretations of quantum mechanics, as well as “hidden variable” modifications of the theory, have proposed several constructions for assigning values to magnitudes (beyond the value assignments defined by the quantum state alone), a variety of theorems exist which impose severe restrictions on such theoretical constructions. This note will deal with Bell's proof (in [2]), that any hidden variable theory satisfying a physically reasonable locality condition is characterized by an inequality which is inconsistent with the quantum statistics. Bell's result has initiated a series of experiments designed to refute the entire class of local hidden variable theories. We show that Bell's inequality actually characterizes a feature of hidden variable theories which is much weaker than locality in the sense considered physically motivated.
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While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and, therefore, do not violate any Bell inequality. We provide an up to date overview of the existing local hidden--variable models for entangled quantum states, both in the bipartite and multipartite case, and discuss some of the most relevant open questions in this context. Our review covers twenty five years of this line of research since the seminal work by Werner [R. F. Werner, Phys. Rev. A 40, 8 (1989)] providing the first example of an entangled state with a local model, which in turn appeared twenty five years after the seminal work by Bell [J. S. Bell, Physics 1, 195 (1964)], about the impossibility of recovering the predictions of quantum mechanics using a local hidden--variables theory.
Abstract Bell’s theorem (Bell 1964) establishes that local hidden variable theories are committed to Bell inequalities violated by quantum correlations. Since violations of Bell inequalities can be verified without requiring that the observables whose correlations figure in the inequalities be measured with arbitrarily high precision, Bell’s theorem yields a method of falsifying local hidden variable the­ ories. Moreover, the evidence for violations of Bell inequalities We thank J. Finklestein, N. D. Mermin, and an anonymous referee for helpful comments. A. K. was supported by a Royal Society University Research Fellow­ ship and thanks the Oxford Centre for Quantum Computation for much appreciated hospitality.