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Quantum entanglement (QE) is one of the most mysterious and promising subjects in physics. With applications in cryptographic space-to-space, space-to-earth and fibre communications, in addition to teleportation and quantum computing, QE goes beyond fascination and into the pragmatic spheres of commerce and the military.
In this monograph the philosophical and physical routes to QE are explained in a methodical and detailed approach. Furthermore, the interferometric approach to the derivation of QE probability amplitudes for a pair and multiple-pairs of quanta is exposed step by step. Written by F J Duarte, an expert in the field of quantum optics, the text provides the first side-by-side description of the philosophical path and the physical path to quantum entanglement, and does so in a clear and cohesive manner. This is also the first book to describe and explain, in a transparent exposition, the interferometric derivation of the ubiquitous probability amplitude for quantum entanglement.
A cool book on a cool topic, Fundamentals of Quantum Entanglement manages to package a complex topic in a series of easier-to-swallow chapters. Of course, there are equations not for the faint of heart and there are the usual challenges of understanding quantum phenomena (with even more daunting math in the appendixes), but the author makes it all fun to read.
This is a mathematically annotated history of science, illustrated with diagrams and backed up by extensive lists of references in each chapter. It is surprising how much the compact size of the chapters helps to give the reader a feeling of swift progress as each chapter is digested. The topics themselves are irresistible for the interested audience: teleportation (not of objects, but of quantum states), quantum communications and, of course, quantum computing—just a brief introduction without prime factoring algorithms.
For readability and for excellent references, as well as for a tiny index, the book works well for anybody interested in the topic, but it lacks the problems that would make it suitable as a textbook.
Bogdan Hoanca 2020 Optics & Photonics News, The Optical Society
1. Introduction
2. Dirac’s contribution
3. The Einstein Podosky Rosen (EPR) paper
4. The Schrödinger papers
5. Wheeler’s paper
6. The probability amplitude for quantum entanglement
7. The quantum entanglement experiment
8. The annihilation quantum entanglement experiments
9. The Bohm and Aharonov paper
10. Bell’s theorem
11. Feynman’s Hamiltonians
12. The second Wu quantum entanglement experiment
13. The hidden variable theory experiments
14. The optical quantum entanglement experiments
15. The quantum entanglement probability amplitude 1947-1992
16. The GHZ probability amplitudes
17. The interferometric derivation of the quantum entanglement probability amplitude for n N 2
18. The interferometric derivation of the quantum entanglement probability amplitude for n N 21, 22, 23, 24… 2r
19. The interferometric derivation of the quantum entanglement probability amplitudes for n N 3, 6
20. What happens with the entanglement at n and N 2
21. Quantum entanglement probability amplitudes and Bell’s theorem
22. Cryptography via quantum entanglement
23. Quantum entanglement and teleportation
24. Quantum entanglement and quantum computing
25. Space-to-space and space-to-Earth communications via quantum entanglement
26. Space-to-space quantum interferometric communications: an alternative to quantum entanglement communications?
27. Quanta pair sources for quantum entanglement experiments
28. More on quantum entanglement
29. On the interpretation of quantum mechanics
Appendices
I. Revisiting the Einstein Podosky Rosen (EPR) paper
II. Revisiting the Pryce-Ward probability amplitude
III. Classical and quantum interference
IV. Interferometers and their probability amplitudes
V. Polarization rotators
VI. Vector products in quantum notation
VII. Trigonometric identities
VIII. More on quantum notation
IX. From quantum principles to classical optics
X. Introduction to Hamilton’s quaternions