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CRC Press eBooks

Quantum Entanglement

F. J. Duarte

Published Apr 10, 2026• 0 citations
Publisher

Abstract

Quantum interference and quantum entanglement are intrinsically ‘entangled’ at the most fundamental strata of quantum mechanics. In fact, John Clive Ward defined the whole of quantum mechanics in the following terms: ‘ the probability amplitude of quantum entanglement … was my first lesson in quantum mechanics, and in a very real sense my last, since all the rest is mere technique, which can be learnt from books. ’ Albeit Ward's opinion is somewhat colored by his ineffable genius, there is no doubt that quantum entanglement is at the foundations of quantum mechanics. Quantum entanglement encapsulates indeterminacy, superposition, and nonlocality with sublime cohesiveness. In this chapter we describe the fine details of the physics of quantum entanglement, free of paradoxes, its interferometric origin, and its generalized character.

DOI
10.1201/9781003649434-8

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Quantum interference and quantum entanglement are intrinsically ‘entangled’ at the most fundamental strata of quantum mechanics. In fact, John Clive Ward defined the whole of quantum mechanics in the following terms: ‘ the probability amplitude of quantum entanglement … was my first lesson in quantum mechanics, and in a very real sense my last, since all the rest is mere technique, which can be learnt from books. ’ Albeit Ward's opinion is somewhat colored by his ineffable genius, there is no doubt that quantum entanglement is at the foundations of quantum mechanics. Quantum entanglement encapsulates indeterminacy, superposition, and nonlocality with sublime cohesiveness. In this chapter we describe the fine details of the physics of quantum entanglement, free of paradoxes, its interferometric origin, and its generalized character.
The experimental origin of quantum mechanics is highlighted, and essential features of the photon are described. The philosophical path to quantum entanglement, as defined by the works of EPR–Bohm and Aharonov–Bell, and the physics path to quantum entanglement, as defined by the works of Dirac–Wheeler–Pryce and Ward, are introduced and discussed. The probability amplitude for quantum Entanglement, discovered in 1947, is then introduced prior to a high-level overview of the field. This introduction then concludes with a chapter-by- chapter description of the book and its purpose.
The experimental origin of quantum mechanics is highlighted and essential features of the photon are described. The philosophical path to quantum entanglement, as defined by the works of EPR to Bohm and Aharonov to Bell, and the physics path to quantum entanglement, as defined by the works of Dirac to Wheeler to Pryce and Ward, are introduced and discussed. The probability amplitude for quantum entanglement, discovered in 1947, is then introduced prior to a high-level overview of the field. The introduction then concludes with a chapter-by-chapter description of this book and its aims.
The quantumness of quantum mechanics is integrated by those properties and characteristics so unique to quantum mechanics that makes it an utterly extraordinary, and fascinating, branch of physics. And the beauty of it is that this quantumness has its origin in the very foundations of quantum physics built on experimental facts and thus they reflect the character of Nature itself. Indeterminacy , indistinguishability , nonlocality , uncertainty , and superposition are not the byproducts of some strange unverified theory but they are the characteristics of a brave experimentally based physics that has been verified by experiment time and time again. Add to this that most of the action in quantum physics takes place via probability amplitudes , that exist in a purely mathematical realm, and you have something superbly unique. Those are the elements that configure the quantumness of quantum mechanics, as discussed and described in this chapter.
Ever since Schrödinger envisioned the possibility of quantum entanglement, in 1935, by contemplating the implications of the meaning of ‘not complete’ emitted by Einstein and colleagues towards quantum mechanics the word paradox has been brought forth. Paradox was again invoked by Bohm in the 1950s and of course the creation of Bell's theorem was motivated by it. Paradox has been a trademark of the philosophical path towards quantum entanglement. And yet, the physics tells us that quantum entanglement is not afflicted at all by any paradox whatsoever. That this was the case was first silently implied by the physics of Dirac, Wheeler, and Pryce and Ward (1930–1947) and directly articulated by Feynman in 1965. Here we transparently show that, from the quantum interference perspective, the physics of quantum entanglement is completely and utterly free of paradoxes.
Quantum entanglement (QE) has rapidly become a subject of great interest in academia, industry, and government research institutions. This book builds on the first edition of Fundamentals of Quantum Entanglement to provide a transparent and more insightful introduction for graduate students, scientists, and engineers. It is also a highly useful education tool for those practitioners that were not aware of the physical origin of quantum entanglement: the Dirac—Wheeler—Pryce—Ward physics. The new edition includes an expansion on topics such as quantum entropy and quantum time. The book provides a direct, practical, and transparent introduction to the principles and physics of quantum entanglement. It does so whilst utilizing an interferometric approach based on Dirac—Feynman superposition probability amplitudes. Part of IOP Series in Coherent Sources, Quantum Fundamentals, and Applications. Key features • Provides an overview of quantum entanglement at a basic level • Explains the philosophical origin of quantum entanglement as well as the physical origin • Presents the key equation for the probability amplitude for QE from three perspectives while emphasizing its interferometric derivation • Includes applications on Quantum Cryptography, Quantum Teleportation, Quantum Computing • Reviews the current technology of QE with an emphasis in space-to-space communications