Quantum Entanglement Engineering and Applications (Coherent Sources and Applications)

✍ Scribed by F J Duarte, Travis Taylor

• Publisher: Iop Publishing Ltd
• Year: 2021
• Tongue: English
• Leaves: 218
• Category: Library

✦ Synopsis

Quantum entanglement (QE) is one of the most, if not the most, mysterious, and yet most promising subjects of current physics. With applications in cryptographic space-to-space, space-to-earth, and fiber communications, in addition to teleportation and quantum computing, QE goes beyond fascination and into the pragmatic spheres of commerce and the military.

With the growing population of engineers in need of a transparent, pragmatic, and direct introduction to QE and its applications, this book, the first of its kind, focuses on the practical mathematical tools necessary to handle QE and its requirements to design optical configurations for QE-based systems. Specific applications include satellite networks, space-to-space communications, quantum teleportation, and quantum computing.

Key Features

• The first and only available text on engineering for quantum entanglement.
• Presents an introduction to the topic and explains the very basic physics concepts.
• Provides a tour of the relevant mathematics essential to handle quantum entanglement.
• Provides content to design optical configurations for optical entanglement-based systems in quantum communications and quantum computing.
• Includes discussions of key practical applications such as space-to-space, fiber and satellite communications.
• Presents the fascinating subject of quantum interpretations as elucidated by quantum entanglement.

✦ Table of Contents

PRELIMS.pdf
Series preface
Book preface
Acknowledgements
Author biographies
F J Duarte
T S Taylor
CH001.pdf
Chapter 1 Introduction
1.1 Introduction
1.2 Essentials of quantum mechanics
1.2.1 The quantum photon
1.2.2 Planck’s constant: h
1.3 Ward’s succinct perspectives
1.4 The philosophy and the physics of quantum entanglement
1.4.1 The philosophy
1.4.2 The physics
1.5 Quantum entanglement as a discipline
1.6 Quantum entanglement engineering and applications
1.7 Intent
Problems
References
CH002.pdf
Chapter 2 Dirac’s notation for quantum entanglement
2.1 Introduction
2.2 Dirac’s bra ket notation
2.3 Dirac’s notation in N-slit interferometers
2.4 Semi coherent interference
2.5 Expanded series of N-slit quantum interference probabilities
2.6 From quantum probabilities to measurable intensities
2.7 Dirac’s identities
2.8 Quantum entanglement probability amplitudes for n = N = 2
2.9 Quantum entanglement probability amplitude for n = N = 4
2.10 Quantum entanglement probability amplitudes for n = N = 8
2.11 Quantum entanglement probability amplitudes for n = N = 16
2.12 Quantum entanglement probability amplitudes for n = N = 21, 22, 23, 24, …, 2r
2.13 Quantum entanglement probability amplitudes for n = N = 3
2.14 Quantum entanglement probability amplitudes for n = N = 6
2.15 Beyond single quanta-pair quantum entanglement
2.16 Discussion
Problems
References
CH003.pdf
Chapter 3 Indistinguishability
3.1 Introduction
3.2 Indistinguishability in quantum interference
3.3 Indistinguishability in Dirac’s identities
3.4 Indistinguishability in quantum entanglement
3.5 Indistinguishability in quanta ensembles
3.6 Discussion
Problems
References
CH004.pdf
Chapter 4 Quantum interferometry via Dirac’s bra ket notation
4.1 Introduction
4.2 The N-slit interferometer
4.3 Interferometers configured by beam splitters
4.3.1 The single-beam splitter
4.3.2 The Mach–Zehnder interferometer
4.3.3 The Michelson interferometer
4.3.4 The Sagnac interferometer
4.4 Beam-splitter matrices and Dirac’s bra ket notation
4.4.1 The beam splitter and the Hadamard gate
4.5 Revisiting the single-beam splitter
4.5.1 The HOM interferometer
Problems
References
CH005.pdf
Chapter 5 Vectors, matrices, and tensors for quantum entanglement
5.1 Introduction
5.2 Vector basics
5.3 Vector products
5.3.1 Dot product
5.3.2 Cross product
5.3.3 The ket bra product
5.3.4 Vector direct product
5.3.5 Vector outer product
5.4 Matrix algebra
5.4.1 The identity matrix
5.4.2 The inverse matrix
5.4.3 The matrix determinant and trace
5.4.4 Eigenvalues and eigenvectors
5.5 The Pauli matrices
5.5.1 Eigenvalues of the Pauli matrices
5.6 Unitary matrices
5.7 The tensor product
Problems
References
CH006.pdf
Chapter 6 Five avenues to the probability amplitude of quantum entanglement
6.1 Introduction
6.2 Ward’s heuristic derivation
6.2.1 The quantum entanglement probability
6.3 Quantum entanglement from Feynman’s two-state approach
6.4 Quantum entanglement from N-slit interference
6.4.1 Additional pair of quantum entanglement states
6.5 Quantum entanglement from the Pauli matrices
6.5.1 Pauli matrices from the Hamiltonian
6.5.2 From Pauli matrices to quantum entanglement states
6.6 Quantum entanglement from the Hadamard gate
6.7 Quantum interference or quantum entanglement?
Problems
References
CH007.pdf
Chapter 7 Quantum entanglement in matrix notation
7.1 Introduction
7.2 Quantum entanglement probability amplitudes
7.3 From ket vectors to polarization matrices
7.4 The Pauli matrices and quantum entanglement
7.5 The Hadamard matrix
7.5.1 Derivation of the matrix for the Hadamard gate
7.6 Optical matrices based on the probability amplitudes of quantum entanglement
7.7 Polarization rotators for quantum entanglement
7.7.1 Wave plates
7.7.2 Rhomboids
7.7.3 Prismatic rotators
7.8 Quantum operations with polarization rotators
7.9 Quantum operations with the Hadamard gate
Problems
References
CH008.pdf
Chapter 8 Quantum entanglement applications
8.1 Introduction
8.2 Classical cryptography concepts
8.3 Quantum entanglement applications to cryptography
8.3.1 Quantum key distribution (QKD)
8.3.2 Experiments
8.3.3 All-quantum security protocol
8.4 Quantum entanglement applications to teleportation
8.4.1 The methodology of teleportation
8.4.2 Technology
8.5 Quantum computing
8.5.1 Pauli gates
8.5.2 The Pauli-X gate and quantum entanglement
8.5.3 The Hadamard gate and quantum entanglement
8.5.4 Technology
8.6 Quantum entanglement applications to metrology
8.7 Overview
Problems
References
CH009.pdf
Chapter 9 Space-to-space quantum communications
9.1 Introduction
9.2 Satellite engineering parameters
9.3 Beam divergence
9.4 Optical configuration for quantum satellite communications
9.4.1 Satellite–satellite
9.4.2 Earth–space–Earth
9.5 Existing data from experiments on quantum satellite communications
9.5.1 The Delingha–Lijiang experiment
9.5.2 The International Space Station experiment
9.6 Satellite networks and their dependence on entangled photon source characteristics
9.6.1 The quantum repeater and quantum data teleportation
9.7 Sources for quantum entanglement communications
9.8 Outlook
Problems
References
CH010.pdf
Chapter 10 Quantum entanglement and the interpretations of quantum mechanics
10.1 Introduction
10.2 Many alternative interpretations
10.3 Guidance from quantum titans
10.3.1 Dirac
10.3.2 Feynman
10.3.3 Dyson
10.3.4 Lamb
10.3.5 Ward
10.4 Hidden variable theories
10.4.1 Bohm’s hidden variable theories
10.4.2 Bell’s theorem
10.4.3 Comment on the EPR paper
10.5 A pragmatic perspective on the interpretations of quantum mechanics
10.6 Quantum principles
10.7 Quantum measurements
10.7.1 Dyson’s first layer quantum mechanics
10.7.2 Dyson’s second layer quantum mechanics
10.7.3 Quantum measurement sequence
10.7.4 Quantum entanglement measurements
10.7.5 The observer
10.7.6 On ‘the collapse of the wave function’
10.8 Is quantum entanglement the essence of quantum mechanics?
10.9 On the origin of the Dirac–Feynman principle
10.10 Quantum pragmatism free of paradoxes
Problems
References
APP1.pdf
Chapter
A.1 Introduction
A.2 The cavity linewidth equation: a heuristic approach
A.3 The cavity linewidth equation: an interferometric approach
A.4 Coherent electrically-pumped organic interferometric emitters
A.4.1 Coherence
A.4.2 The quantum perspective
A.5 Quantum interference and classical interference
A.5.1 Classical interference
A.5.2 Quantum interference
A.5.3 From quantum to classical
A.6 Intracavity double-mode beating instability
A.6.1 Alternative double-mode instability characterization
A.6.2 Mode intensities
A.7 Dirac’s ‘coincidences’
Problems
References
INDEX.pdf
Index