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UNIVERSITY OF CALGARY Telecommunication Components for Fast Quantum Key Distribution by Itzel Lucio Martinez A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF PHYSICS AND ASTRONOMY CALGARY,ALBERTA May, 2008 © Itzel Lucio Martinez 2008 Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-44272-2 Our file Notre reference ISBN: 978-0-494-44272-2 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission. In compliance with the Canadian Conformement a la loi canadienne Privacy Act some supporting sur la protection de la vie privee, forms may have been removed quelques formulaires secondaires from this thesis. ont ete enleves de cette these. While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. Canada Abstract Quantum Key Distribution in combination with the one-time pad encryption protocol promises unconditional secure communication. However, current Quantum Key Distribution (QKD) systems distribute keys with low rates, making the implementation of the highly key consum­ ing one-time pad impractical. This thesis describes a detailed characterization of telecommu­ nication components in view of possible use for high rate QKD through telecommunication fibre networks, and a proof-of-principle demonstration of a QKD system using the compo­ nents studied. Specific problems have been identified, and solutions are suggested Acknowledgements I would like to thank my supervisor, Dr. Wolfgang Tittel, for all his guidance, help, patience and great sense of humor throughout the duration of this work. I would also like to thank Xiaofan Mo, a postdoc in our group, for all of his time, advice, help and for making the lab an enjoyable place. I would like to thank Steve Hosier and Philip Chan, members of the QC2 group and the Quantum Cryptography project for their help in all sort of things during this work. I would specially like to thank my family, Tofio, Alejandrina and Jose Luis, for their encouragement and support throughout my life, without them I would not be who I am today. I would like to thank Tim for all the delicious meals and many good moments we have shared that have made my time in Canada so enjoyable. I would like to thank Michael S., Mike D., Georg, Frank and all the people in IQIS that have shared their friendship with me. I could not forget all my coworkers in the QC2 group (Gina, Ahdiyeh, Josh, Allison, Cecilia, Erhan, Felix, John, Mike, Neil and Vladimir) who create such a pleasant atmosphere in the office and the lab. Finally, I would like to thank CONACyT and the Mexican public education system for giving me, and many other Mexican people, the opportunity to improve our quality of life. m Table of Contents Abstract ii Acknowledgements iii Table of Contents iv List of Tables vii List of Figures viii 1 Introduction 1 1.1 Background 1 1.2 Classical Cryptography 2 1.2.1 Asymmetric Cryptography 2 1.2.2 Public-Key Cryptography 3 1.2.3 Classical symmetric-key cryptography 4 1.2.4 Advanced Encryption Standard 6 1.3 Key Distribution 7 1.4 Quantum Cryptography 8 1.5 This work 9 1.5.1 Motivation 9 1.5.2 Organization 11 2 Quantum Key Distribution (QKD) 12 2.1 Quantum key distribution protocols 12 2.1.1 BB84 12 2.1.2 Ekert91 14 2.1.3 BBM92 14 2.2 Classical Post-processing 15 2.2.1 Error Correction 16 2.2.2 Privacy Amplification 17 2.3 Eavesdropping 18 2.3.1 Qubit attacks 18 2.3.2 Individual attacks 20 2.3.3 Coherent attacks 21 2.3.4 Photon number splitting attack 22 2.3.5 Other channel attacks 28 2.4 Experimental QKD: The State of the Art 29 2.4.1 Fiber-based QKD 29 2.4.2 Free-Space QKD 31 2.4.3 Networking 32 3 Experimental investigations 33 3.1 The set-up 33 3.1.1 Alice 33 3.1.2 Bob 36 3.2 Components 37 3.2.1 The Laser Diodes 37 3.2.2 Intensity Modulator 41 iv V 3.2.3 The Phase Modulator 42 3.2.4 Polarization Controller 47 3.2.5 Single Photon Detector 49 3.3 Quantum Key Distribution 52 3.3.1 Measurement of the QBER and Key generation rate 52 4 Discussion 55 4.1 Components 55 4.1.1 Laser Diode 55 4.1.2 Intensity Modulator 55 4.1.3 Phase Modulator 58 4.1.4 Polarization Stabilizer 59 4.1.5 Single Photon Detector 59 4.2 Performance of the QKD system 60 4.2.1 Decoy State protocol 60 4.2.2 Detector noise based distance limitations 61 5 Summary and Outlook 62 Bibliography 65 vi Glossary a Absorption coefficient r\ Quantum efficiency of single photon detectors A Wavelength H Signal state (mean photon number of 0.5) v\ First decoy state (mean photon number of 0.1) vQ Second decoy state (vacuum state) AES Advanced Encryption Standard (symmetric cryptosystem) APD Avalanche Photodiode Att Attenuator AWG Arbitrary Waveform Generator BS Beamsplitter CG Clock Generator Det Detector e Quantum bit error rate e\ Single photon pulse error rate eM Multi-photon pulse error rate FM Faraday mirror Y12 Shannon entropy IM Intensity modulator LDc Classical laser diode LDQ Quantum laser diode LDPC Low density parity check n Index of refraction P Power PD Dark count probability of a single photon detector PBS Polarization Beam Splitter PM Phase modulator PSY Polarization synthesizer/analyzer (polarization controller) Qi Single photon detection rate Qn Signal state detection rate Qv Decoy state detection rate QBER Quantum bit error rate QKD Quantum Key Distribution RSA Rivest, Shamir and Adleman (asymmetric cryptosystem) s Secret key yield per sifted key SPD Single Photon Detector t Transmission coefficient TDC Time-to-digital converter V Voltage Yi Conditional probability of a detection event for an i-photon state sent Y0 Background rate List of Tables 1.1 Encryption using the one-time pad 5 1.2 Comparision of classical cryptographic schemes 7 3.1 Dark counts and Quantum Efficiency for 4 different detectors 50 3.2 Results of the measurements of the QBER for signal and decoy states 54 4.1 Single photon gain and error rate assessed via decoy states 61 vn List of Figures 2.1 Polarization states represented on the Poincare sphere 13 2.2 Flow diagram showing Quantum Key Distribution 19 2.3 Information vs. QBER 22 2.4 The plug-and-play system 30 2.5 Free-space QKD 31 3.1 The entire QKD system 34 3.2 Classical header and quantum data 35 3.3 Alice's setup 36 3.4 Bob's setup 37 3.5 Screen shots of LD pulses 38 3.6 Measurement of output power stability of quantum and classical LD 39 3.7 Measurement of polarization stability and extinction ratio of the quantum LD 40 3.8 Intensity modulator 41 3.9 Measurement of the output power stability of the IM 42 3.10 Phase modulator 43 3.11 Measurement of the polarization extinction ratio of the PM 44 3.12 Performance of the PM 46 3.13 Working principle of the PSY 47 3.14 Compensation of polarization transformation with a PSY 48 3.15 Time response of a PSY for compensating polarization transformation. ... 49 3.16 Measurement of afterpulses 51 3.17 Our QKD system 53 4.1 Home-made IM 56 via Chapter 1 Introduction Cryptography is the science of hiding the meaning of a message. The purpose of a cryp­ tographic system is to help a party, typically called Alice, to send a message to a receiver, Bob, using a public channel, and to prevent the eavesdropper, Eve, from learning the message when eavesdropping the transmission. 1.1 Background A possible solution to the problem of secret communication, besides cryptography, is steganog- raphy which consists in hiding the message rather than hiding the meaning of it. The security of the information transmitted relies on the security of the message. An example can be the story of Demeratus who sent a warning about a forthcoming attack to Greece by writing it on a wooden panel and covering it in wax [1], In order to better understand cryptography, I will introduce some of the terminology used in this field.
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