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Defeating Eavesdropping with Quantum Illumination

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Defeating Eavesdropping with Quantum Illumination Defeating Eavesdropping with Quantum Illumination by Wenbang Xu Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of OF TECHOLCYV Electrical Engineer MA R 20 at the 2 MASSACHUSETTS INSTITUTE OF TECHNOLOGY ES.RA.. ARCHIVES February 2012 @ Massachusetts Institute of Technology 2012. All rights reserved. A uthor ............................... Department of Electrical Engineering and Computer Science January 17, 2012 (2 hA ,11 IQ Certified by.... Jeffrey H. Shapiro Julius A. Stratton Professor of Electrical Engineering Thesis Supervisor Accepted by ....... Ieslie ATholodziejski Chair, Department Committee on Graduate Theses Defeating Eavesdropping with Quantum Illumination by Wenbang Xu Submitted to the Department of Electrical Engineering and Computer Science on January 15, 2012, in partial fulfillment of the requirements for the degree of Electrical Engineer Abstract Quantum illumination is a paradigm for using entanglement to gain a performance advantage-in comparison with classical-state systems of the same optical power- over lossy, noisy channels that destroy entanglement. Previous work has shown how it can be used to defeat passive eavesdropping on a two-way Alice-to-Bob-to-Alice communication protocol, in which the eavesdropper, Eve, merely listens to Alice and Bob's transmissions. This thesis extends that work in several ways. First, it derives a lower bound on information advantage that Alice enjoys over Eve in the passive eavesdropping scenario. Next, it explores the performance of alternative practical receivers for Alice, as well as various high-order modulation formats for the passive eavesdropping case. Finally, this thesis extends previous analysis to consider how Alice and Bob can minimize their vulnerability to Eve's doing active eavesdropping, i.e., when she injects her own light into the channel. Thesis Supervisor: Jeffrey H. Shapiro Title: Julius A. Stratton Professor of Electrical Engineering 4 Acknowledgments I truly appreciate my research advisor, Prof. Jeffrey H. Shapiro, for his patience during my research in the quantum communication group. Professor Shapiro always promotes students to explore new and interesting topics. At the same time, he helps them in great detail due to his rigorous background and abundant experience in physics and information theory. His guidance will benefit me in my professional career forever. I would like to thank Dr. Franco N.C. Wong for setting up my office, answering my questions, and teaching me about experiments. I would especially like to thank Tian Zhong and Dheera Venkatraman for answering some fundamental questions about quantum physics when I joined this group. Discussing the phase-lock experiment platform with Tian was an extremely interesting experience for me. I also thank Prof. Dennis Freeman for giving me the opportunity to teach 6.003, Signals and Systems. This teaching experience has taught me how to actively guide students. I am grateful for having a great family. My family members-including my wife, Xiuping, Zhang, my brother, Jinbang, Xu and my sisters-are always behind me. Whatever I do, they always support me. When I decided to quit an excellent job and study at MIT, all of them encouraged me to chase my dream and enjoy my life at MIT. This research was supported by an Office of Naval Research Basic Research Chal- lenge Grant. I would like to thank them for that support. 6 Contents 1 Introduction 1.1 Classical Communication Theory .... .............. .. 1.2 Quantum Communication ........... ............ 1.3 Thesis Structure ....................... ....... 2 Background Material 21 2.1 Electromagnetic Field Modes ...... ...... 22 2.2 Operators and States ........... ...... 24 2.3 Photodetection Statistics ......... .. .... 27 2.4 Optical Amplifiers .. .... .. .... 29 2.5 Classical versus Nonclassical States ... ...... 29 2.6 Spontaneous Parametric Downconversion .. .... 31 2.7 Minimum Error-Probability Detection. ...... 32 3 Passive Eavesdropping 3.1 Passive Attack Communication Protocol ...... ....... ... 3.2 Information Disparity between Alice and Eve .......... .... 3.3 Alternative Receivers ......... ............ ...... 3.4 M-ary Modulation Technique .... ............ ...... 4 Active Eavesdropping 4.1 Active Case I: Eve Injects Light without Modifying Channel Transmit- tivities .... ....... ....... ....... ........ .. 4.2 Active Case II: Eve Modifies the Alice-to-Bob and Bob-to-Alice Channels 64 4.3 Active case III: Eve Injects Light Undetectable by Power Monitoring 67 5 Conclusions and Future Work 73 5.1 Conclusions ................................ 73 5.2 Future W ork ................................ 74 List of Figures 1-1 Schematic of basic communication system. ... .... ..... ... 12 1-2 Schematic of quantum-illumination two-way communication protocol- showing modal annihilation operators-with passive-eavesdropper Eve receiving all the light that does not reach its intended destination. The annihilation operator notation for the optical modes will be explained in Chapter 3. .. ...... ...... ..... ...... ...... 18 2-1 Schematic of idealized direct detection, q is the electron charge. .. 27 2-2 Schematic of idealized homodyne detection. ..... ...... ... 27 2-3 Schematic of idealized heterodyne detection. ..... ...... 28 3-1 Schematic of quantum-illumination two-way communication protocol- showing modal annihilation operators-with passive-eavesdropper Eve receiving all the light that does not reach its intended destination. 36 3-2 Error-probability bounds for Ns = 0.004, r, = 0.1, and GB = NB = 10'. Solid curves: Chernoff upper bounds for Alice and Eve's optimum quantum receivers. Dashed curve: error-probability lower bound for Eve's optimum quantum receiver. Dot-dashed curve: Bhattacharyya upper bound for Alice's OPA receiver. ..... ...... ...... 41 3-3 Error-probability performance of Alice's OPA receiver for Ns = 0.004, K = 0.1, and GB = NB = 104 . Solid curve: Gaussian approximation for Pr(e). Dashed curve: Bhattacharyya upper bound for Pr(e). Dot- dashed curve: Bhattacharyya lower bound for Pr(e). .... ..... 43 3-4 Alice's Shannon information and upper bound on Eve's Holevo infor- mation per channel use for Ns = 0.004, . = 0.1, and GB = NB = 104. Solid curve: Lower bound between Alice's Shannon information and Eve's Holevo information. Dashed curve: Shannon information for Alice's OPA receiver. Dot-dashed curve: upper bound on Holevo in- formation for Eve's optimum quantum receiver. ........... 45 3-5 Error Probability for Alice's OPA receiver for Ns = 0.004, r = 0.1, and GB = NB = 10 4 . Dashed curve: single-output OPA receiver. Solid curve: dual-output OPA receiver. ... ............ ..... 49 3-6 Schematic of Alice's Beam Splitter Receiver. ...... ........ 50 3-7 Error probabilities for Alice's several practical receivers assuming Ns = 0.004, , = 0.1, and GB = NB = 10 4 . Dotted curve: heterodyne re- ceiver for aR and ar. Solid curve: single-output OPA receiver. Dashed and dot dashed curves: upper and lower bounds for single-output beam splitter receiver. .... ............ ........... ... 52 3-8 Decision regions for QPSK quantum illumination with heterodyne de- tection ... ...... ...... ...... ...... ...... .. 56 3-9 QPSK signal constellation ................... ..... 58 4-1 Alice and Eve's OPA Receiver Performance . ...... ....... 70 4-2 Schematic of realistic quantum-illumination two-way communication protocol with active-eavesdropper Eve using an SPDC source and an OPA receiver. .. ........ ........ ....... ...... 71 4-3 Error probability versus bit rate for Alice and Eve's OPA receivers. Lower bound on the error probability of Eve's optimum quantum re- ceiver for passive eavesdropping is also included. ........... 72 Chapter 1 Introduction Communication is the process by which information is transmitted from one location to another. It is an essential need and a fundamental practice of the world. For ex- ample, to discuss a business idea with your friend, you might talk to him face to face, which is a process of interpersonal communication. However, such interpersonal com- munications is not possible when a long distance separates the communicating parties. To solve the problem of long-distance communication, human beings have invented many communication systems to conquer distance. In ancient times, runners car- ried messages from one place to another. People lit giant fires on mountain summits or beacon towers, or rang bells to communicate impending attacks. Long-distance communication became much easier, however, with the advent of electromagnetic techniques, such as Morse's development of the telegraph early in the 19th century. Later that century, Maxwell's theory of electromagnetic waves and Hertz's experi- mental verification relieved the need for wires to carry telegraph signals, leading to Popov and Marconi's invention of the radio-telegraph technique in 1883. At roughly the same time, electromagnetic communication moved beyond the telegraph and into voice communication when Bell patented the telephone in 1876. The preceding technological advances dramatically improved long-distance com- munications, but they did not address the fundamental limits on information trans- mission. Then, in 1948, Claude Shannon published his historic paper "A Mathemati- cal Theory of Communication" [1], establishing the theoretical foundation for classical communication systems. Since then, technology and theory have advanced together, allowing ubiquitous communications-in
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