Fundamentals of Quantum Entanglement

PRELIMS.pdf
Preface
Acknowledgments
Author biography
F J Duarte
CH001.pdf
Chapter 1 Introduction
1.1 Introduction
1.2 A few words on quantum mechanics
1.2.1 The photon from a quantum perspective
1.3 Ward’s observation
1.4 History of quantum entanglement
1.4.1 The philosophical path
1.4.2 The physics path
1.5 The field of quantum entanglement
1.6 Fundamentals of Quantum Entanglement
1.7 Intent
References
CH002.pdf
Chapter 2 Dirac’s contribution
2.1 Introduction
2.2 Dirac’s pair theory
2.3 Dirac’s notation
2.4 Dirac’s notation in N-slit interferometers
2.5 Semi coherent interference
2.6 From quantum probabilities to measurable intensities
2.7 Dirac’s identities
References
CH003.pdf
Chapter 3 The Einstein–Podolsky–Rosen (EPR) paper
3.1 Introduction
3.2 EPR’s doubts on quantum mechanics
3.3 EPR’s definition of a correct theory
References
CH004.pdf
Chapter 4 The Schrödinger papers
4.1 Introduction
4.2 The first Schrödinger paper
4.3 The second Schrödinger paper
References
CH005.pdf
Chapter 5 Wheeler’s paper
5.1 Introduction
5.2 Wheeler’s paper’s significance to quantum theory
5.3 Wheeler’s paper’s significance to quantum experiments
References
CH006.pdf
Chapter 6 The probability amplitude for quantum entanglement
6.1 Introduction
6.2 The Pryce–Ward paper
6.2.1 Theoretical legacy of the Pryce–Ward paper
6.2.2 Experimental legacy of the Pryce–Ward paper
6.3 Ward’s doctoral thesis
6.4 Summary
References
CH007.pdf
Chapter 7 The quantum entanglement experiment
7.1 Introduction
7.2 The quantum entanglement experiment
7.3 Historical notes
References
CH008.pdf
Chapter 8 The annihilation quantum entanglement experiments
8.1 Introduction
8.2 The first three quantum entanglement experiments
8.3 Further significance of the annihilation experiments
References
CH009.pdf
Chapter 9 The Bohm and Aharonov paper
9.1 Introduction
9.2 Significance to the development of quantum entanglement research
9.3 Philosophy and physics
References
CH010.pdf
Chapter 10 Bell’s theorem
10.1 Introduction
10.2 von Neumann’s work
10.3 Bell’s theorem or Bell’s inequalities
10.4 An additional perspective on Bell’s theorem
10.5 Example
10.6 More philosophy and physics
References
CH011.pdf
Chapter 11 Feynman’s Hamiltonians
11.1 Introduction
11.2 Probability amplitudes via Hamiltonians à la Feynman
11.3 Arrival to quantum entanglement probability amplitudes
11.4 Discussion
References
CH012.pdf
Chapter 12 The second Wu quantum entanglement experiment
12.1 Introduction
12.2 Salient features
12.3 Bell’s theorem and hidden variables
References
CH013.pdf
Chapter 13 The hidden variable theory experiments
13.1 Introduction
13.2 Testing for local hidden variable theories
13.3 Early optical experiment
13.4 Observations and discussion
References
CH014.pdf
Chapter 14 The optical quantum entanglement experiments
14.1 Introduction
14.2 The Aspect experiments
14.2.1 The first Aspect experiment
14.2.2 The second Aspect experiment
14.2.3 The third Aspect experiment
14.3 Observations and discussion
References
CH015.pdf
Chapter 15 The quantum entanglement probability amplitude 1947–1992
15.1 Introduction
15.2 The quantum entanglement probability amplitude 1947–92
15.2.1 1947–9
15.2.2 1948
15.2.3 1951
15.2.4 1957
15.2.5 1975
15.2.6 1990
15.2.7 1992
15.3 Observations and discussion
References
CH016.pdf
Chapter 16 The GHZ probability amplitudes
16.1 Introduction
16.2 The GHZ probability amplitudes
16.3 Observations and discussion
References
CH017.pdf
Chapter 17 The interferometric derivation of the quantum entanglement probability amplitude for n = N = 2
17.1 Introduction
17.2 The meaning of the Dirac–Feynman probability amplitude
17.3 The derivation of the quantum entanglement probability amplitude
17.4 Identical states of polarization
17.5 Discussion
References
CH018.pdf
Chapter 18 The interferometric derivation of the quantum entanglement probability amplitude for n = N = 21, 22, 23, 24, … 2r
18.1 Introduction
18.2 The quantum entanglement probability amplitude for n = N = 4
18.3 The quantum entanglement probability amplitude for n = N = 8
18.4 The quantum entanglement probability amplitude for n = N = 16
18.5 The quantum entanglement probability amplitude for n = N = 21, 22, 23, 24…2r
18.6 Discussion
References
CH019.pdf
Chapter 19 The interferometric derivation of the quantum entanglement probability amplitudes for n = N = 3, 6
19.1 Introduction
19.2 The quantum entanglement probability amplitude for n = N = 3
19.3 The quantum entanglement probability amplitude for n = N = 6
19.4 Discussion
References
CH020.pdf
Chapter 20 What happens with the entanglement at n = 1 and N = 2?
20.1 Introduction
20.2 Reversibility: from entanglement to interference
20.3 Schematics
20.4 Experimental and theoretical perspectives
20.4.1 Experimental perspective
20.4.2 Theoretical perspective
20.5 Interference for N slits and n = 1
References
CH021.pdf
Chapter 21 Quantum entanglement probability amplitudes and Bell’s theorem
21.1 Introduction
21.2 Probability amplitudes
21.3 Quantum polarization
21.4 Quantum probabilities and Bell’s theorem
21.5 Example
21.6 Discussion
References
CH022.pdf
Chapter 22 Cryptography via quantum entanglement
22.1 Introduction
22.2 Measurement protocol
22.3 Experiments
References
CH023.pdf
Chapter 23 Quantum entanglement and teleportation
23.1 Introduction
23.2 The mechanics of teleportation
23.3 Technology
References
CH024.pdf
Chapter 24 Quantum entanglement and quantum computing
24.1 Introduction
24.2 Entropy
24.3 Qbits
24.4 Quantum entanglement and Pauli matrices
24.5 Pauli matrices and quantum entanglement
24.6 Quantum gates
24.6.1 Pauli gates
24.6.2 The Hadamard gate
24.7 The Hadamard matrix and quantum entanglement
24.8 Multiple entangled states
24.9 Technology
References
CH025.pdf
Chapter 25 Space-to-space and space-to-Earth communications via quantum entanglement
25.1 Introduction
25.2 Space-to-space configurations
25.3 The space-to-Earth experiment
25.4 Further horizons
References
CH026.pdf
Chapter 26 Space-to-space quantum interferometric communications: an alternative to quantum entanglement communications?
26.1 Introduction
26.2 The generalized N-slit quantum interference equations
26.3 The generation and transmission of interferometric characters
26.4 The inherent quantum security mechanism
26.5 Discussion
References
CH027.pdf
Chapter 27 Quanta pair sources for quantum entanglement experiments
27.1 Introduction
27.2 Positron–electron annihilation
27.3 Atomic Ca emission
27.4 Type I SPDC
27.5 Type II SPDC
27.6 Further horizons
References
CH028.pdf
Chapter 28 More on quantum entanglement
28.1 Introduction
28.2 Consequences of the EPR paper
28.3 Hidden variable theories
28.4 The perspectives of EPR and Schrödinger on quantum entanglement
28.5 Indistinguishability and Dirac’s identities
28.6 Photon non-locality
28.7 Discussion
References
CH029.pdf
Chapter 29 On the interpretation of quantum mechanics
29.1 Introduction
29.2 Quantum critical
29.2.1 On ‘The moral aspects of quantum mechanics’
29.2.2 On ‘Against measurement’
29.3 Pragmatic perspective
29.4 Fundamental principles
29.5 The Dirac–Feynman–Lamb doctrine
29.6 The importance of the probability amplitude
29.7 The best interpretation of quantum mechanics
29.8 Discussion
References
APP1.pdf
Chapter
A.1 Introduction
A.2 EPR and the uncertainty principle
A.3 Conclusion
References
APP2.pdf
Chapter
B.1 Introduction
B.2 Exciting times and extreme succinctness
B.3 Conclusion
References
APP3.pdf
Chapter
C.1 Introduction
C.2 The classical interference equation
C.3 The N-slit interferometer
C.4 The difference between classical and quantum interference
References
APP4.pdf
Chapter
D.1 Introduction
D.2 Interferometers
D.2.1 The Mach–Zehnder interferometer
D.2.2 The Michelson interferometer
D.2.3 The Sagnac interferometer
D.2.4 The N-slit interferometer
D.3 Beam splitter matrices
References
APP5.pdf
Chapter
E.1 Introduction
E.2 Wave plates
E.3 Rhomboid and prismatic rotators
References
APP6.pdf
Chapter
F.1 Introduction
F.2 Vector products
F.2.1 Dot product
F.2.2 Cross product
F.2.3 Density matrix
F.2.4 Vector direct product
F.2.5 Vector outer product
F.2.6 Kronecker product or tensor product
F.3 Equivalence in vector notation for entangled polarizations
F.4 The Hadamard matrix and quantum entanglement
References
APP7.pdf
Chapter
G.I Trigonometric identities
APP8.pdf
Chapter
H.1 Introduction
H.2 Certainly not classical
H.3 Multiplication of probability amplitudes
References
APP9.pdf
Chapter
I.1 Introduction
I.2 From quantum interference to generalized diffraction
I.3 From generalized diffraction to generalized refraction
I.4 From generalized refraction to reflection
I.5 From quantum interference to Heisenberg’s uncertainty principle
I.6 The cavity linewidth equation
I.7 Generalized multiple-prism dispersion
I.7.1 Generalized multiple-prism dispersion for laser pulse compression
I.8 Discussion
References
APP10.pdf
Chapter
J.1 Introduction
J.2 Basic quaternion identities
References
INDEX.pdf
Index