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<p>Foreword ix</p> <p>Preface xi</p> <p>Introduction xiii</p> <p><b>Chapter 1. The State of the Art in Quantum Communications </b><b>1</b></p> <p>1.1. Quantum mechanics as a generalized probability theory 1</p> <p>1.2. Contextuality 3</p> <p>1.3. Indeterminism and contextuality 3</p> <p>1.4. Contextuality and hidden variables 4</p> <p>1.5. Non-locality and contextuality 5</p> <p>1.6. Bell states 6</p> <p>1.7. Violation of the Leggett–Garg inequality 7</p> <p>1.8. Violation of the Bell inequality 8</p> <p>1.9. EPR paradox 8</p> <p><b>Chapter 2. Concepts in Communications </b><b>13</b></p> <p>2.1. Quantum limits 13</p> <p>2.2. Qubits 15</p> <p>2.3. Qudit and qutrit 20</p> <p>2.3.1. Qudit 20</p> <p>2.3.2. Qutrit 23</p> <p>2.4. Pauli matrices 24</p> <p>2.4.1. Definition 24</p> <p>2.4.2. Properties of these matrices 25</p> <p>2.5. Decoherence 26</p> <p>2.6. Entanglement 28</p> <p><b>Chapter 3. Quantum Signal Processing </b><b>31</b></p> <p>3.1. Wigner distribution 32</p> <p>3.2. Quantum Fourier transform 34</p> <p>3.3. Gauss sums in a quantum context 36</p> <p>3.4. Geometry for quantum processing 37</p> <p><b>Chapter 4. Quantum Circuits </b><b>41</b></p> <p>4.1. Reversible logic 41</p> <p>4.1.1. Physical reversibility 41</p> <p>4.2. Reversible circuits 42</p> <p>4.2.1. Reversible calculation models 42</p> <p>4.2.2. Reversibility in quantum calculation 43</p> <p>4.3. Quantum gates 44</p> <p>4.3.1. Hadamard gate 44</p> <p>4.3.2. Pauli-X gate 45</p> <p>4.3.3. Pauli-Y gate 45</p> <p>4.3.4. Pauli-Z gate 46</p> <p>4.3.5. Swap gate 46</p> <p>4.4. Toffoli gate 47</p> <p>4.5. Deutsch gate 48</p> <p>4.6. Quantum dots 49</p> <p>4.7. QCA 52</p> <p><b>Chapter 5. Optical Fibers and Solitons </b><b>53</b></p> <p>5.1. Introduction 53</p> <p>5.2. Optical fibers 54</p> <p>5.2.1. The fiber’s parameters 55</p> <p>5.2.2. Birefringence in optical fibers 58</p> <p>5.2.3. Dispersion in optical fibers 58</p> <p>5.3. Soliton solutions for differential equations 60</p> <p>5.3.1. Introduction 60</p> <p>5.3.2. Nonlinear Schrodinger equation 61</p> <p>5.3.3. Focusing soliton oscillations 63</p> <p>5.3.4. Wave packet autostriction (modulation instability) 65</p> <p>5.3.5. Evolution of the initial disturbance 69</p> <p>5.4. Conclusion 73</p> <p><b>Chapter 6. Photonic Crystals </b>75</p> <p>6.1. General introduction 75</p> <p>6.2.1. Photonic crystals with one dimension (Bragg network) 77</p> <p>6.2.2. Band diagram 80</p> <p>6.2.3. Maps of forbidden bands 81</p> <p>6.3. Three-dimensional photonic crystals 82</p> <p>6.4. Filters and multiplexors 82</p> <p>6.5. Add-drop filters 83</p> <p>6.6. Digital methods for photonic crystal analysis 84</p> <p>6.6.1. Introduction 84</p> <p>6.6.2. Modeling periodic dielectric structures 85</p> <p>6.6.3. FDTD method 85</p> <p>6.6.4. Available digital tools 86</p> <p>6.7. Conclusion 88</p> <p><b>Chapter 7. ROADM</b> <b>89</b></p> <p>7.1. Technological advances 89</p> <p>7.2. “Router”-type filter 90</p> <p><b>Chapter 8. WDM </b><b>95</b></p> <p>8.1. Operating principle 95</p> <p>8.2. Using WDM systems 96</p> <p>8.3. DWDM networks 98</p> <p><b>Chapter 9. Quantum Algorithms </b><b>99</b></p> <p><b>Chapter 10. Applications</b><b> 101</b></p> <p>10.1. Laser satellites 101</p> <p>10.1.1. The Doppler effect in inter-satellite laser communications 102</p> <p>10.1.2. Modeling the Doppler effect in inter-satellite laser communications 103</p> <p>10.1.3. Calculation software 108</p> <p>10.1.4. Calculation software 108</p> <p><b>Chapter 11. Quantum Cryptography</b><b> 121</b></p> <p>11.1. Cloning photons 123</p> <p>11.2. Quantum cryptography 123</p> <p>11.2.1. Introduction 123</p> <p>11.2.2. Methodology 124</p> <p>11.2.3. Results and discussion 126</p> <p>11.2.4. Conclusion 129</p> <p>11.3. Solutions to the practical limits of quantum cryptography 130</p> <p>11.3.1. Introduction 130</p> <p>11.3.2. Theoretical considerations 130</p> <p>11.3.3. Practical considerations 131</p> <p>11.3.4. Quantum noise 132</p> <p>11.3.5. The QBER in quantum transmissions 133</p> <p>11.3.6. Error correction methods in quantum cryptography 138</p> <p>11.3.7. The correcting code for error correction in BB84 140</p> <p>11.3.8. Time coding for error correction in BB84 142</p> <p>11.3.9. Conclusion 144</p> <p>11.4. Quantum error correcting codes 145</p> <p>11.4.1. Introduction 145</p> <p>11.4.2. Classical error correcting code 145</p> <p>11.4.3. Quantum error correcting code 148</p> <p>11.4.4. The time coding method for error correction: application in BB84 157</p> <p>11.4.5. Correction of time code errors using the repetition method 158</p> <p>11.4.6. Conclusion 161</p> <p>Conclusion 163</p> <p>Bibliography 167</p> <p>Index 179</p>

"This book explores the technological advances in quantum communications, with a special focus on telecommunications systems. It includes three main sections— a comprehensive review of the state of the art in quantum communications, an analysis of current and future circuitry, and quantum signal processing ... The book has an excellent conclusion and can be used as a rich research resource suitable for graduate students as well as researchers in the field." <b>Optics and Photonics News website, 2017</b>

<p><b>Malek Benslama</b> is currently Head of the Doctoral School of Space Telecommunications and a member of the scientific council of the Algerian Space Agency.</p> <p><b>Achour Benslama</b> is currently Professor of theoretical physics at the University of Constantine 1 in Algeria. <p><b>Skander Aris</b> is Associate Professor at the University of Constantine 1 in Algeria and Head of the electronics department.

<p>Computers are quickly making the transition from silicon towards miniaturization, which now risks reaching its limits as dictated by the laws of physics. Quantum communications are the answer to post-silicon computers.</p> <p>The main applications for quantum communications in the domain of telecommunications are beginning to appear, with some commercial applications already on the market. <p>This book explores the technological advances in quantum communications with a special focus on telecommunications systems. <p>The authors provide a comprehensive state of the art on quantum communications and quantum signal processing. The reader will learn about the advantages, current applications and future prospects of quantum technology.

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