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Document Title Universidade de Aveiro Departamento de Física, 2010 Steven Comunicações Seguras usando Criptografia Ramos Quântica Carneiro Secure Communications based on Quantum Cryptography “Nobody understands quantum theory.” — Richard P. Feyman Universidade de Aveiro Departamento de Física, 2010 Steven Comunicações Seguras usando Criptografia Ramos Quântica Carneiro Secure Communications based on Quantum Cryptography Dissertação apresentada à Universidade de Aveiro para cumprimento dos requesitos necessários à obtenção do grau de Mestre em Engenharia Física, realizada sob a orientação científica do Professor Doutor Armando Humberto Moreira Nolasco Pinto, Professor Auxiliar do Departamento de Engenharia Electrónica, Telecomunicações e Informática da Universidade de Aveiro e Investigador Auxiliar do Instituto de Telecomunicações - Pólo de Aveiro, e sob a orientação científica do Professor Doutor Rogério Nunes Nogueira, Investigador Auxiliar do Instituto de Telecomunicações - Pólo de Aveiro. o júri / the jury presidente / president Prof. Dr. João de Lemos Pinto Professor Catedrático da Universidade de Aveiro (por delegação do Reitor da Universidade de Aveiro) vogais / examiners committee Prof. Dr. Armando Humberto Moreira Nolasco Pinto Professor Auxiliar da Universidade de Aveiro (orientador/advisor) Prof. Dr. Rogério Nunes Nogueira Investigador Auxiliar do Instituto de Telecomunicações - Pólo de Aveiro (co-orientador/co- advisor) Prof. Dr. Manuel Joaquim Bastos Marques Professor Auxiliar da Faculdade de Ciências da Universidade do Porto acknowledgements There are many people I would like to thank. First, I would like to thank Prof. Dr. Armando Humberto Moreira Nolasco Pinto, for the oportunity to work on this project and all his support throughout its ongoing. I would also like to thank Prof. Dr. Rogério Nunes Nogueira, for several important scientific discussions and advice during this project. Many thanks to my collegues M. Sc. Nuno Alexandre Peixoto Silva and M. Sc. Nelson Jesus Cordeiro Muga for several scientific discussions which revealed important for the outcome of this project. A special thanks to M. Sc. Álvaro José Caseiro de Almeida, for all his support and dedication during this project, and many important scientific discussions throughout this project. Without him, none of this would have been possible. I would also like to acknowledge the Universidade de Aveiro and the Instituto de Telecomunicações, where I was given all the support needed to carry out this work; to "QuantTel - Quantum Secure Telecommunications" and "QuantPrivTel - Quantum Private Telecommunications" for all the technical support offered, to perform my experimental trials. Last, but certaintly not least, I would like to thank my parents, for all their love and support during this important chapter of my life. I dedicate this to them. Thank you all! resumo No trabalho apresentado, estudamos criptografia quântica, nomeadamente formas de geração, transmissão e detecção de pares de fotões entrelaçados. Para uma melhor compreensão dos processos e fenómenos que estão na sua base, abordamos o paradoxo de Einstein, Podolsky e Rosen (EPR) e a teoria de Bell. Estas teo- rias possibilitaram-nos investigar sobre a natureza física, local ou não local a nível quântico, tendo sido as respostas obtidas essenciais para a segurança e confidencial- idade na transmissão de dados. Depois, exploramos os vários tipos de processos de geração de fotões entrelaçados, concentrando-nos num tipo de processo em particular, a mistura de quatro ondas. Com a base teórica já estabelecida, apresen- tamos uma montagem experimental na qual geramos, transmitimos e detectamos fotões entrelaçados através da mistura espontânea de quatro ondas. Após uma descrição pormenorizada da montagem experimental, focando nas várias etapas e de algumas particularidades da experiência realizada, apresentamos os resultados obtidos. Nesta experiência usámos 2 tipos de fibras: uma fibra com o zero de dis- persão deslocado (DSF) e uma fibra altamente não linear (HNLF), comparando e analisando as diferenças entre elas e a sua contribuição para a experiência em causa. Por fim, apresentamos as conclusões deste trabalho e também o trabalho que poderá ser realizado no futuro. abstract In the present thesis, we study quantum cryptography, namely the generation pro- cesses and, how we can transmit and detect entangled photon pairs. To understand the processes and phenomena which leads us to the core of our work, we look at the Einstein, Podolsky and Rosen paradox (EPR), and the Bell theory for answers. These two theories give us the means to question the locality or nonlocality of physical reality regarding quantum systems, which is of the utmost importance when we consider information security in data transmission. With this, we present several processes to generate entangled photon pairs, focusing on one in particular, Four-Wave Mixing (FWM). With the theoretical groundwork laid out, we present our setup to create, transmit and detect entangled photon pairs using spontaneous four-wave mixing. After a detailed description of our setup, describing the purpose and importance of each stage, we present the obtained results. In this experiment, we use two fibers: a Dispersion-Shifted Fiber (DSF) and a highly nonlinear fiber Highly Nonlinear Fiber (HNLF), comparing the results reached with each fiber. In the final chapter, we present our conclusions and the work that can be done in the near future. List of Acronyms IDEA International Data Encryption Algorithm AES Advanced Encryption Standard RSA A cryptographic protocol by Rivest, Shamir and Adler PGP Pretty Good Privacy protocol OTP one-time pad EPR Three important physicists: Albert Einstein, Boris Podolsky and Nathan Rosen which questioned quantum mechanics QKD Quantum Key Distribution SPM Self-Phase Modulation XPM Cross-Phase Modulation FWM Four-Wave Mixing BB84 BB84 is a quantum cryptographic protocol by Charles Bennet and Gilles Brassard, presented in 1984 E91 E91 is a quantum cryptographic protocol by Arthur Ekert, presented in 1991 COW Coherent One Way protocol QND Quantum Nondemolition QDC Quantum Direct Communincation PDC Parametric Down-Conversion SFWM Stimulated Four-Wave Mixing SpFWM Spontaneous Four-Wave Mixing SARG04 SARG04 is a cryptographic protocol devised by Scarani et al, similar to the BB84 protocol CHSH Physicists John Clauser, Holt, Abe Shimony and Michael Horne, which formulated the CHSH inequality TLS Tunable Laser Source FBG Fiber Bragg Grating PC Polarization Controller PC1 Polarization Controller 1 MZ Mach-Zehnder modulator DC Direct Current ii EDFA Erbium Doped Fiber Amplifier FWHM Full Width at Half Maximum PC2 Polarization Controller 2 LP Linear Polarizer PBS Polarizing Beam Splitter AWG Arrayed Waveguide Grating QWP Quarter Wave Plate HWP Half Wave Plate RLP Rotating Linear Polarizer RLP Rotating Linear Polarizer 1 APD Avalanche Photodiode Detector APD1 Avalanche Photodiode Detector 1 APD2 Avalanche Photodiode Detector 2 TIA Time Interval Analyzer ASE Amplified Spontaneous Emission FFC Fiber to Fiber Coupler SMF Single-Mode Fiber WP Waveplates CW Continous Wave DSF Dispersion-Shifted Fiber HNLF Highly Nonlinear Fiber GVD Group Velocity Dispersion TTM8 Time Tagging Module 8 FPGA Field Programmable Gate Arrays PA Polarization Analyzers MUX Optical Multiplexer SpRS Spontaneous Raman Scattering iii List of Symbols + parallel measuring basis, page 17 + photon emergence, page 11 − no photon emergence, page 11 − orthogonal measuring basis, page 17 A generic observable, page 9 A generic physical quantity, page 10 A site A, page 11 Aeff Effective area, page 28 B generic physical quantity, page 10 B site B, page 11 C correlation between objects, page 13 C(n) number of correlated events, page 17 D displacement field, page 7 D polynomial elements, page 25 Dn(x) decryption process, page 1 E electric field, page 7 E expectancy value, page 13 En(x) encryption operation, page 1 H magnetic field, page 22 J Jone’s matrix, page 10 Leff effective length, page 28 Leff fiber length, page 28 Leff nonlinear parameter, page 28 N photon counts, page 34 Nmax maximum counts, page 35 Nmin minimum counts, page 35 P polarization field, page 7 P1(θ1) generic probability, page 11 iv P2(θ2) generic probability, page 11 Pj(θj) probability of a photon being detected in arm j, page 10 P12(θ1; θ2) joint probability of both photons being detected when polarizers are in position, page 10 Pdc dark count proabability, page 30 R reflectivity, page 22 R ring radius, page 29 S Shannon entropy, page 14 T transmission matrix, page 10 Vπ maximum voltage bias, page 25 X generic observable, page 16 Y generic observable, page 16 ∆L pathway difference, page 29 ∆S Shannon entropy error, page 35 ∆v velocity uncertainty, page 9 ∆φ optical path, page 24 ∆φ phase shift, page 24 Λ probability space, page 13 α ellipticity, page 35 α fiber absorption, page 28 α1 detector efficiency, page 11 \ maximum violation angles, page 34 \ orthogonal basis, page 34 \ parallel basis, page 34 A¯ diference of A, page 15 B¯ diference of B, page 15 x¯ mean value, page 34 β angle set basis, page 35 χ electrical suceptibility, page 7 χ(1) first order electrical suceptibility, page 7 χ(2) second order electrical suceptibility, page 7 χ(3) third order electrical suceptibility, page 4 χ(i) ith order electrical suceptibility, page 7 δ eccentricity, page 10 0 fiela amplitude after polarizer, page 11 v x abscissa versor, page 10 y ordenate versor, page 10 ηD detector efficiency, page 30 γDSF nonlinear parameter for a dispersion-shifted fiber, page 28 γHNLF
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