Fundamentals of Quantum Entanglement

PRELIMS.pdf
Series preface
Book preface
Acknowledgement
Author biography
F J Duarte
CH001.pdf
Chapter 1 Introduction
1.1 Introduction
1.2 Foundations of quantum mechanics
1.2.1 The mathematical bases of quantum mechanics
1.2.2 The photon from a quantum perspective
1.3 Ward’s observations
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
Problems
References
CH002.pdf
Chapter 2 Dirac’s physics
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 Expanded series of N-slit quantum interference probabilities
2.6 The interferometric probability in 2D and 3D
2.7 Semi-coherent interference
2.8 From quantum probabilities to measurable intensities
2.9 Interferometric calculations and quantum coherence
2.10 Dirac’s identities
2.10.1 Indistinguishability identities
2.10.2 Extending the emission identities
Problems
References
CH003.pdf
Chapter 3 The Einstein–Podolsky–Rosen (EPR) paper
3.1 Introduction
3.2 EPR’s doubts on quantum mechanics
3.2.1 EPR’s definition of a correct theory
3.3 Transparent resolution of the EPR ‘paradox’
3.3.1 EPR and the uncertainty principle
Problems
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 significance to quantum theory
5.3 Wheeler’s paper significance to quantum experiments
5.4 A theoretical opportunity
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
Problems
References
CH007.pdf
Chapter 7 The quantum entanglement experiment
7.1 Introduction
7.2 The quantum entanglement experiment
7.3 Historical notes
Problem
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
Problems
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
Problems
References
CH010.pdf
Chapter 10 Bell’s theorem
10.1 Introduction
10.2 von Neumann’s prediction
10.3 Bell’s theorem or Bell’s inequalities
10.4 Example
10.5 An additional perspective on Bell’s theorem
10.6 More philosophy and physics
Problems
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 Hyperfine splitting
11.5 Discussion
Problems
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
Problems
References
CH015.pdf
Chapter 15 The quantum entanglement probability amplitude 1947–1992
15.1 Introduction
15.2 The quantum entanglement probability amplitude 1947–1992
15.2.1 1947–1949
15.2.2 1948
15.2.3 1951
15.2.4 1957
15.2.5 1965
15.2.6 1975
15.2.7 1990
15.2.8 1992
15.3 Observations and discussion
Problems
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 Beyond single quanta-pair quantum entanglement
17.6 Discussion
Problems
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
Problems
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
Problems
References
CH020.pdf
Chapter 20 Quantum 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
20.4.3 Derivation of the Dirac–Feynman principle
20.5 Interference for N slits and n = 1
Problems
References
CH021.pdf
Chapter 21 Quantum entanglement probability amplitudes applied to Bell’s theorem
21.1 Introduction
21.2 Probability amplitudes
21.3 Quantum polarization
21.4 Quantum probabilities and Bell’s theorem
21.5 Application to Bell’s theorem
21.6 All-quantum approach
21.7 Discussion
Problems
References
CH022.pdf
Chapter 22 Quantum entanglement via matrix notation
22.1 Introduction
22.2 The probability amplitudes of quantum entanglement
22.3 Dirac’s ket vectors and Pauli matrices
22.4 Quantum entanglement in Pauli matrix notation
22.4.1 Mechanics of Pauli matrices
22.5 Quantum entanglement and the Hadamard gate
22.6 Complete set of matrices derived from the probability amplitudes of quantum entanglement
22.7 Polarization rotators for quantum entanglement
22.8 Quantum mathematics with polarization rotators
22.9 Quantum mathematics with the Hadamard gate
22.10 Interconnectivity in quantum mechanics
Problems
References
CH023.pdf
Chapter 23 Cryptography via quantum entanglement
23.1 Introduction
23.2 Measurement protocol based on Bell’s theorem
23.2.1 Experiments
23.3 All-quantum measurement protocol
Problems
References
CH024.pdf
Chapter 24 Quantum entanglement and teleportation
24.1 Introduction
24.2 The mechanics of teleportation
24.3 Technology
Problems
References
CH025.pdf
Chapter 25 Quantum entanglement and quantum computing
25.1 Introduction
25.2 Entropy
25.3 Qbits
25.4 Quantum entanglement and Pauli matrices
25.5 Pauli matrices and quantum entanglement
25.6 Quantum gates
25.6.1 Pauli gates
25.6.2 The Hadamard gate
25.7 The Hadamard matrix and quantum entanglement
25.8 Multiple entangled states
25.9 Technology
Problems
References
CH026.pdf
Chapter 26 Space-to-space and space-to-Earth communications via quantum entanglement
26.1 Introduction
26.2 Space-to-space configurations
26.3 Experiments
26.3.1 The space-to-earth experiment
26.3.2 The International Space Station experiment
26.4 Further horizons
Problems
References
CH027.pdf
Chapter 27 Space-to-space quantum interferometric communications
27.1 Introduction
27.2 The generalized N-slit quantum interference equations
27.3 The generation and transmission of interferometric characters
27.4 The inherent quantum security mechanism
27.5 Discussion
Problems
References
CH028.pdf
Chapter 28 Quanta pair sources for quantum entanglement experiments
28.1 Introduction
28.2 Positron–electron annihilation
28.3 Atomic Ca emission
28.4 Type I spontaneous parametric down-conversion
28.5 Type II spontaneous parametric down-conversion
28.6 Quantum description of parametric down-conversion
28.7 Alternative quantum pair sources
28.8 Further horizons
Problems
References
CH029.pdf
Chapter 29 Quantum interferometric principles
29.1 Introduction
29.2 Fundamental principles of quantum mechanics
29.3 Nonlocality of the photon
29.4 Indistinguishability and Dirac’s identities
29.5 Quantum measurements
29.5.1 Probability amplitudes
29.5.2 Quantum probabilities
29.5.3 Quantum entanglement measurements
29.5.4 Quantum time and entropy
29.5.5 The quantum measurer
29.6 Quantum entanglement at the foundations of quantum mechanics
29.7 On the origin of the Dirac–Feynman principle
29.7.1 Optimum finesse
29.7.2 Further refinements
29.8 Discussion
Problems
References
CH030.pdf
Chapter 30 On the interpretation of quantum mechanics
30.1 Introduction
30.2 Philosophical aspects of quantum entanglement
30.2.1 The perspectives of EPR and Schrödinger on quantum entanglement
30.2.2 Hidden variable theories
30.3 Quantum critical
30.3.1 On ‘The moral aspects of quantum mechanics’
30.3.2 On ‘Against measurement’
30.3.3 On Bell’s criticisms of quantum mechanics
30.4 Conceptual ‘problems’ in quantum mechanics
30.4.1 The ‘measurement problem’
30.4.2 Particle–wave duality
30.4.3 Quantum reality
30.4.4 Unnecessary concerns
30.5 Quantum luminaries
30.6 The pragmatic perspective
30.7 The Dirac–Feynman–Lamb doctrine
30.8 The all-important probability amplitude
30.9 The quantumness derived from the nonlocality of the photon
30.10 The best interpretation of quantum mechanics
30.11 Discussion
Problems
References
APPA.pdf
Chapter
A.1 Introduction
A.2 Exciting times and extreme succinctness
A.3 Conclusion
References
APPB.pdf
Chapter
B.1 Introduction
B.2 The classical interference equation
B.3 The N-slit quantum interference
B.4 From quantum interference to classical interference
Problems
References
APPC.pdf
Chapter
C.1 Introduction
C.2 Interferometers
C.2.1 The Mach–Zehnder interferometer
C.2.2 The Michelson interferometer
C.2.3 The Sagnac interferometer
C.2.4 The N-slit interferometer
C.3 Beam splitter matrices and Dirac’s bra ket notation
C.3.1 The beam splitter and the Hadamard gate
C.3.2 The Hanbury Brown–Twist interferometer
C.3.3 The HOM interferometer
Problems
References
APPD.pdf
Chapter
D.1 Introduction
D.2 Wave plates
D.3 Rhomboid polarization rotators
D.4 Multiple-prism broadband collinear polarization rotators
Problems
References
APPE.pdf
Chapter
E.1 Introduction
E.2 Vector basics
E.3 Vector products
E.3.1 Dot product
E.3.2 Cross product
E.3.3 The ket bra product
E.3.4 Vector direct product
E.3.5 Vector outer product
E.4 Matrix algebra
E.4.1 The identity matrix
E.4.2 The inverse matrix
E.4.3 The matrix determinant and trace
E.4.4 Eigenvalues and eigenvectors
E.4.5 Eigenvalues and eigenvectors of the Pauli matrices
E.5 Unitary matrices
E.6 The tensor product
E.7 Equivalence in vector notation for entangled polarizations
Problems
References
APPF.pdf
Chapter
F.1 Trigonometric identities
Problems
References
APPG.pdf
Chapter
G.1 Introduction
G.2 Certainly not classical
G.3 Multiplication of probability amplitudes
G.4 On the Dirac identity for quantum entanglement
References
APPH.pdf
Chapter
H.1 Introduction
H.2 From quantum interference to generalized diffraction
H.3 From generalized diffraction to generalized refraction
H.4 From generalized refraction to reflection
H.5 From quantum interference to Heisenberg’s uncertainty principle
H.6 The cavity linewidth equation
H.7 Generalized multiple-prism dispersion
H.7.1 Generalized multiple-prism dispersion for laser pulse compression
H.8 Discussion
Problems
References
APPI.pdf
Chapter
I.1 Introduction
I.2 Complex conjugates
I.3 Basic quaternion identities
Problems
References
APPJ.pdf
Chapter
J.1 Introduction
J.2 Planck’s constant
J.3 The fine structure constant
J.4 The extreme weakness of gravity in the quantum domain
J.5 Quantum consciousness
J.6 Fundamental physics constants
Problems
References
INDEX.pdf
Index