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

"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." Optics and Photonics News website, 2017

• Foreword ixPreface xiIntroduction xiiiChapter 1. The State of the Art in Quantum Communications 11.1. Quantum mechanics as a generalized probability theory 11.2. Contextuality 31.3. Indeterminism and contextuality 31.4. Contextuality and hidden variables 41.5. Non-locality and contextuality 51.6. Bell states 61.7. Violation of the Leggett–Garg inequality 71.8. Violation of the Bell inequality 81.9. EPR paradox 8Chapter 2. Concepts in Communications 132.1. Quantum limits 132.2. Qubits 152.3. Qudit and qutrit 202.3.1. Qudit 202.3.2. Qutrit 232.4. Pauli matrices 242.4.1. Definition 242.4.2. Properties of these matrices 252.5. Decoherence 262.6. Entanglement 28Chapter 3. Quantum Signal Processing 313.1. Wigner distribution 323.2. Quantum Fourier transform 343.3. Gauss sums in a quantum context 363.4. Geometry for quantum processing 37Chapter 4. Quantum Circuits 414.1. Reversible logic 414.1.1. Physical reversibility 414.2. Reversible circuits 424.2.1. Reversible calculation models 424.2.2. Reversibility in quantum calculation 434.3. Quantum gates 444.3.1. Hadamard gate 444.3.2. Pauli-X gate 454.3.3. Pauli-Y gate 454.3.4. Pauli-Z gate 464.3.5. Swap gate 464.4. Toffoli gate 474.5. Deutsch gate 484.6. Quantum dots 494.7. QCA 52Chapter 5. Optical Fibers and Solitons 535.1. Introduction 535.2. Optical fibers 545.2.1. The fiber’s parameters 555.2.2. Birefringence in optical fibers 585.2.3. Dispersion in optical fibers 585.3. Soliton solutions for differential equations 605.3.1. Introduction 605.3.2. Nonlinear Schrodinger equation 615.3.3. Focusing soliton oscillations 635.3.4. Wave packet autostriction (modulation instability) 655.3.5. Evolution of the initial disturbance 695.4. Conclusion 73Chapter 6. Photonic Crystals 756.1. General introduction 756.2.1. Photonic crystals with one dimension (Bragg network) 776.2.2. Band diagram 806.2.3. Maps of forbidden bands 816.3. Three-dimensional photonic crystals 826.4. Filters and multiplexors 826.5. Add-drop filters 836.6. Digital methods for photonic crystal analysis 846.6.1. Introduction 846.6.2. Modeling periodic dielectric structures 856.6.3. FDTD method 856.6.4. Available digital tools 866.7. Conclusion 88Chapter 7. ROADM 897.1. Technological advances 897.2. “Router”-type filter 90Chapter 8. WDM 958.1. Operating principle 958.2. Using WDM systems 968.3. DWDM networks 98Chapter 9. Quantum Algorithms 99Chapter 10. Applications 10110.1. Laser satellites 10110.1.1. The Doppler effect in inter-satellite laser communications 10210.1.2. Modeling the Doppler effect in inter-satellite laser communications 10310.1.3. Calculation software 10810.1.4. Calculation software 108Chapter 11. Quantum Cryptography 12111.1. Cloning photons 12311.2. Quantum cryptography 12311.2.1. Introduction 12311.2.2. Methodology 12411.2.3. Results and discussion 12611.2.4. Conclusion 12911.3. Solutions to the practical limits of quantum cryptography 13011.3.1. Introduction 13011.3.2. Theoretical considerations 13011.3.3. Practical considerations 13111.3.4. Quantum noise 13211.3.5. The QBER in quantum transmissions 13311.3.6. Error correction methods in quantum cryptography 13811.3.7. The correcting code for error correction in BB84 14011.3.8. Time coding for error correction in BB84 14211.3.9. Conclusion 14411.4. Quantum error correcting codes 14511.4.1. Introduction 14511.4.2. Classical error correcting code 14511.4.3. Quantum error correcting code 14811.4.4. The time coding method for error correction: application in BB84 15711.4.5. Correction of time code errors using the repetition method 15811.4.6. Conclusion 161Conclusion 163Bibliography 167Index 179

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

"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." Optics and Photonics News website, 2017

• Foreword ixPreface xiIntroduction xiiiChapter 1. The State of the Art in Quantum Communications 11.1. Quantum mechanics as a generalized probability theory 11.2. Contextuality 31.3. Indeterminism and contextuality 31.4. Contextuality and hidden variables 41.5. Non-locality and contextuality 51.6. Bell states 61.7. Violation of the Leggett–Garg inequality 71.8. Violation of the Bell inequality 81.9. EPR paradox 8Chapter 2. Concepts in Communications 132.1. Quantum limits 132.2. Qubits 152.3. Qudit and qutrit 202.3.1. Qudit 202.3.2. Qutrit 232.4. Pauli matrices 242.4.1. Definition 242.4.2. Properties of these matrices 252.5. Decoherence 262.6. Entanglement 28Chapter 3. Quantum Signal Processing 313.1. Wigner distribution 323.2. Quantum Fourier transform 343.3. Gauss sums in a quantum context 363.4. Geometry for quantum processing 37Chapter 4. Quantum Circuits 414.1. Reversible logic 414.1.1. Physical reversibility 414.2. Reversible circuits 424.2.1. Reversible calculation models 424.2.2. Reversibility in quantum calculation 434.3. Quantum gates 444.3.1. Hadamard gate 444.3.2. Pauli-X gate 454.3.3. Pauli-Y gate 454.3.4. Pauli-Z gate 464.3.5. Swap gate 464.4. Toffoli gate 474.5. Deutsch gate 484.6. Quantum dots 494.7. QCA 52Chapter 5. Optical Fibers and Solitons 535.1. Introduction 535.2. Optical fibers 545.2.1. The fiber’s parameters 555.2.2. Birefringence in optical fibers 585.2.3. Dispersion in optical fibers 585.3. Soliton solutions for differential equations 605.3.1. Introduction 605.3.2. Nonlinear Schrodinger equation 615.3.3. Focusing soliton oscillations 635.3.4. Wave packet autostriction (modulation instability) 655.3.5. Evolution of the initial disturbance 695.4. Conclusion 73Chapter 6. Photonic Crystals 756.1. General introduction 756.2.1. Photonic crystals with one dimension (Bragg network) 776.2.2. Band diagram 806.2.3. Maps of forbidden bands 816.3. Three-dimensional photonic crystals 826.4. Filters and multiplexors 826.5. Add-drop filters 836.6. Digital methods for photonic crystal analysis 846.6.1. Introduction 846.6.2. Modeling periodic dielectric structures 856.6.3. FDTD method 856.6.4. Available digital tools 866.7. Conclusion 88Chapter 7. ROADM 897.1. Technological advances 897.2. “Router”-type filter 90Chapter 8. WDM 958.1. Operating principle 958.2. Using WDM systems 968.3. DWDM networks 98Chapter 9. Quantum Algorithms 99Chapter 10. Applications 10110.1. Laser satellites 10110.1.1. The Doppler effect in inter-satellite laser communications 10210.1.2. Modeling the Doppler effect in inter-satellite laser communications 10310.1.3. Calculation software 10810.1.4. Calculation software 108Chapter 11. Quantum Cryptography 12111.1. Cloning photons 12311.2. Quantum cryptography 12311.2.1. Introduction 12311.2.2. Methodology 12411.2.3. Results and discussion 12611.2.4. Conclusion 12911.3. Solutions to the practical limits of quantum cryptography 13011.3.1. Introduction 13011.3.2. Theoretical considerations 13011.3.3. Practical considerations 13111.3.4. Quantum noise 13211.3.5. The QBER in quantum transmissions 13311.3.6. Error correction methods in quantum cryptography 13811.3.7. The correcting code for error correction in BB84 14011.3.8. Time coding for error correction in BB84 14211.3.9. Conclusion 14411.4. Quantum error correcting codes 14511.4.1. Introduction 14511.4.2. Classical error correcting code 14511.4.3. Quantum error correcting code 14811.4.4. The time coding method for error correction: application in BB84 15711.4.5. Correction of time code errors using the repetition method 15811.4.6. Conclusion 161Conclusion 163Bibliography 167Index 179

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

"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." Optics and Photonics News website, 2017

• Foreword ixPreface xiIntroduction xiiiChapter 1. The State of the Art in Quantum Communications 11.1. Quantum mechanics as a generalized probability theory 11.2. Contextuality 31.3. Indeterminism and contextuality 31.4. Contextuality and hidden variables 41.5. Non-locality and contextuality 51.6. Bell states 61.7. Violation of the Leggett–Garg inequality 71.8. Violation of the Bell inequality 81.9. EPR paradox 8Chapter 2. Concepts in Communications 132.1. Quantum limits 132.2. Qubits 152.3. Qudit and qutrit 202.3.1. Qudit 202.3.2. Qutrit 232.4. Pauli matrices 242.4.1. Definition 242.4.2. Properties of these matrices 252.5. Decoherence 262.6. Entanglement 28Chapter 3. Quantum Signal Processing 313.1. Wigner distribution 323.2. Quantum Fourier transform 343.3. Gauss sums in a quantum context 363.4. Geometry for quantum processing 37Chapter 4. Quantum Circuits 414.1. Reversible logic 414.1.1. Physical reversibility 414.2. Reversible circuits 424.2.1. Reversible calculation models 424.2.2. Reversibility in quantum calculation 434.3. Quantum gates 444.3.1. Hadamard gate 444.3.2. Pauli-X gate 454.3.3. Pauli-Y gate 454.3.4. Pauli-Z gate 464.3.5. Swap gate 464.4. Toffoli gate 474.5. Deutsch gate 484.6. Quantum dots 494.7. QCA 52Chapter 5. Optical Fibers and Solitons 535.1. Introduction 535.2. Optical fibers 545.2.1. The fiber’s parameters 555.2.2. Birefringence in optical fibers 585.2.3. Dispersion in optical fibers 585.3. Soliton solutions for differential equations 605.3.1. Introduction 605.3.2. Nonlinear Schrodinger equation 615.3.3. Focusing soliton oscillations 635.3.4. Wave packet autostriction (modulation instability) 655.3.5. Evolution of the initial disturbance 695.4. Conclusion 73Chapter 6. Photonic Crystals 756.1. General introduction 756.2.1. Photonic crystals with one dimension (Bragg network) 776.2.2. Band diagram 806.2.3. Maps of forbidden bands 816.3. Three-dimensional photonic crystals 826.4. Filters and multiplexors 826.5. Add-drop filters 836.6. Digital methods for photonic crystal analysis 846.6.1. Introduction 846.6.2. Modeling periodic dielectric structures 856.6.3. FDTD method 856.6.4. Available digital tools 866.7. Conclusion 88Chapter 7. ROADM 897.1. Technological advances 897.2. “Router”-type filter 90Chapter 8. WDM 958.1. Operating principle 958.2. Using WDM systems 968.3. DWDM networks 98Chapter 9. Quantum Algorithms 99Chapter 10. Applications 10110.1. Laser satellites 10110.1.1. The Doppler effect in inter-satellite laser communications 10210.1.2. Modeling the Doppler effect in inter-satellite laser communications 10310.1.3. Calculation software 10810.1.4. Calculation software 108Chapter 11. Quantum Cryptography 12111.1. Cloning photons 12311.2. Quantum cryptography 12311.2.1. Introduction 12311.2.2. Methodology 12411.2.3. Results and discussion 12611.2.4. Conclusion 12911.3. Solutions to the practical limits of quantum cryptography 13011.3.1. Introduction 13011.3.2. Theoretical considerations 13011.3.3. Practical considerations 13111.3.4. Quantum noise 13211.3.5. The QBER in quantum transmissions 13311.3.6. Error correction methods in quantum cryptography 13811.3.7. The correcting code for error correction in BB84 14011.3.8. Time coding for error correction in BB84 14211.3.9. Conclusion 14411.4. Quantum error correcting codes 14511.4.1. Introduction 14511.4.2. Classical error correcting code 14511.4.3. Quantum error correcting code 14811.4.4. The time coding method for error correction: application in BB84 15711.4.5. Correction of time code errors using the repetition method 15811.4.6. Conclusion 161Conclusion 163Bibliography 167Index 179