Quantum Communications in New Telecommunications Systems 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. The main applications for quantum communications in the domain of telecommunications are beginning to appear, with some commercial applications already on the market. This book explores the technological advances in quantum communications with a special focus on telecommunications systems. 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.

Table of Contents:
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 6.2.1. 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