Title Details

Foreword ix

Preface  xi

Introduction xiii

Chapter 1. The State of the Art in Quantum Communications 1

1.1. Quantum mechanics as a generalized probability theory  1

1.2. Contextuality  3

1.3. Indeterminism and contextuality 3

1.4. Contextuality and hidden variables  4

1.5. Non-locality and contextuality  5

1.6. Bell states  6

1.7. Violation of the Leggett–Garg inequality  7

1.8. Violation of the Bell inequality  8

1.9. EPR paradox  8

Chapter 2. Concepts in Communications  13

2.1. Quantum limits 13

2.2. Qubits  15

2.3. Qudit and qutrit  20

2.3.1. Qudit  20

2.3.2. Qutrit  23

2.4. Pauli matrices 24

2.4.1. Definition 24

2.4.2. Properties of these matrices 25

2.5. Decoherence  26

2.6. Entanglement  28

Chapter 3. Quantum Signal Processing  31

3.1. Wigner distribution  32

3.2. Quantum Fourier transform  34

3.3. Gauss sums in a quantum context  36

3.4. Geometry for quantum processing  37

Chapter 4. Quantum Circuits  41

4.1. Reversible logic  41

4.1.1. Physical reversibility 41

4.2. Reversible circuits 42

4.2.1. Reversible calculation models  42

4.2.2. Reversibility in quantum calculation  43

4.3. Quantum gates 44

4.3.1. Hadamard gate  44

4.3.2. Pauli-X gate  45

4.3.3. Pauli-Y gate  45

4.3.4. Pauli-Z gate  46

4.3.5. Swap gate 46

4.4. Toffoli gate 47

4.5. Deutsch gate  48

4.6. Quantum dots 49

4.7. QCA  52

Chapter 5. Optical Fibers and Solitons  53

5.1. Introduction  53

5.2. Optical fibers  54

5.2.1. The fiber’s parameters  55

5.2.2. Birefringence in optical fibers  58

5.2.3. Dispersion in optical fibers  58

5.3. Soliton solutions for differential equations 60

5.3.1. Introduction  60

5.3.2. Nonlinear Schrodinger equation 61

5.3.3. Focusing soliton oscillations 63

5.3.4. Wave packet autostriction (modulation instability) 65

5.3.5. Evolution of the initial disturbance 69

5.4. Conclusion 73

Chapter 6. Photonic Crystals  75

6.1. General introduction  75

6.2. Photonic crystals  76

6.2.1. Photonic crystals with one dimension (Bragg network) 77

6.2.2. Band diagram 80

6.2.3. Maps of forbidden bands 81

6.3. Three-dimensional photonic crystals 82

6.4. Filters and multiplexors  82

6.5. Add-drop filters  83

6.6. Digital methods for photonic crystal analysis  84

6.6.1. Introduction  84

6.6.2. Modeling periodic dielectric structures 85

6.6.3. FDTD method 85

6.6.4. Available digital tools  86

6.7. Conclusion 88

Chapter 7. ROADM 89

7.1. Technological advances  89

7.2. “Router”-type filter  90

Chapter 8. WDM  95

8.1. Operating principle  95

8.2. Using WDM systems 96

8.3. DWDM networks 98

Chapter 9. Quantum Algorithms  99

Chapter 10. Applications 101

10.1. Laser satellites  101

10.1.1. The Doppler effect in inter-satellite laser communications  102

10.1.2. Modeling the Doppler effect in inter-satellite laser communications  103

10.1.3. Calculation software 108

10.1.4. Calculation software 108

Chapter 11. Quantum Cryptography  121

11.1. Cloning photons 123

11.2. Quantum cryptography 123

11.2.1. Introduction 123

11.2.2. Methodology 124

11.2.3. Results and discussion 126

11.2.4. Conclusion  129

11.3. Solutions to the practical limits of quantum cryptography 130

11.3.1. Introduction 130

11.3.2. Theoretical considerations 130

11.3.3. Practical considerations 131

11.3.4. Quantum noise  132

11.3.5. The QBER in quantum transmissions 133

11.3.6. Error correction methods in quantum cryptography 138

11.3.7. The correcting code for error correction in BB84  140

11.3.8. Time coding for error correction in BB84 142

11.3.9. Conclusion  144

11.4. Quantum error correcting codes 145

11.4.1. Introduction 145

11.4.2. Classical error correcting code 145

11.4.3. Quantum error correcting code 148

11.4.4. The time coding method for error correction: application in BB84 157

11.4.5. Correction of time code errors using the repetition method  158

11.4.6. Conclusion  161

Conclusion 163

Bibliography 167

Index 179