Quantum Entanglement Engineering and Applications

F. J. Duarte and T. S. Taylor, Quantum Entanglement Engineering and Applications (Institute of Physics, Bristol, 2021)

ISBN: 978-0-7503-3405-1

10 chapters, 1 appendix, 72 figures, 79 problems, approximately 860 equations, in 200 pages.

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1.1 Introduction

1.2 Essentials of quantum mechanics

1.2.1 The quantum photon

1.2.2 Planckís constant: h

1.3 Wardís 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



2. Diracís notation for quantum entanglment

2.1 Introduction

2.2 Diracís bra ket notation

2.3 Diracís 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 identities

2.8 Quantum entanglement probability amplitudes for n = N = 2

2.9 Quantum entanglement probability amplitudes 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



3. Indistinguishability

3.1 Introduction

3.2 Indistinguishability in quantum interference

3.3 Indistinguishability in Diracís identities

3.4 Indistinguishability in quantum entanglement

3.5 Indistinguishability in quantum ensembles

3.6 Discussion



4.Quantum interferometry via Diracís 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 Diracís bra ket notation

4.4.1 The beam splitter and the Hadamard gate

4.5 Revisiting the single beam splitter



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 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



6. Five avenues to the probability amplitude of quantum entanglement

6.1 Introduction

6.2 Wardís heuristic derivation

6.2.1 The quantum entanglement probability

6.3 Quantum entanglement from Feynmanís two state approach

6.4 Quantum entanglement from N-slit interference

6.5 Quantum entanglement from the Pauli matrices

6.6 Quantum entanglement from the Hadamard gate

6.7 Quantum interference or quantum entanglement?



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 Rhombois

7.7.3 Prismatic rotators

7.8 Quantum operations with polarization rotators

7.9 Quantum operations with the Hadamard gate



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 Mathematical methodology

8.4.2 Technology

8.5 Quantum computing

8.51 The 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



9. Space-to-space quantum communications

9.1 Introduction

9.2 Relevant 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



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 Bohmís hidden variable theories

10.4.2 Bellís 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 Dysonís first layer quantum mechanics

10.7.2 Dysonís second layer quantum mechanics Time flow

10.7.3 Quantum measurement sequence

10.7.4 Quantum entanglement measurements

10.7.5 The observer

10.7.6 On Ďthe collapse of the wave functioní

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




A. More on Diracís notation: application to laser cavities and interference

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 to classical interference

A.5.1 Classical interference

A.5.2 Quantum interference

A.6 Intracavity double-mode beating instability

A.6.1 Alternative double-mode instability characterization

A.7 Diracís Ďcoincidencesí



Page published on the 20th of September, 2021

Updated on the 20th of September, 2019