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研究生: 顏嘉漢
Chia-Han Yen
論文名稱: 帶有量子電傳的量子金鑰分配
Quantum Key Distribution with Teleportation
指導教授: 呂忠津
Chung-Chin Lu
口試委員:
學位類別: 碩士
Master
系所名稱: 電機資訊學院 - 電機工程學系
Department of Electrical Engineering
論文出版年: 2005
畢業學年度: 93
語文別: 中文
論文頁數: 51
中文關鍵詞: 量子金鑰分配量子電傳量子糾纏金鑰安全性
外文關鍵詞: Quantum key distribution, Quantum teleportation, Quantum entanglement, key, security
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  • 密碼學(Cryptography)的應用於人類生活中扮演重要的角色; 的密碼專家所遇到的挑戰是,如何讓發送者與接收者共同擁有一把鑰匙,並保證不會外流(key distribution)。我們通常用一種稱為「公開金鑰加密法」(public-key cryptography)的方法發送「秘密鑰匙」(簡稱密鑰或私鑰),對傳送的訊息加密或解密。
    然而,隨著量子資訊的來臨,量子電腦的快速運算可以輕易地破解傳統密碼的演算法。量子金鑰分配(Quantum key distribution)使用了量子力學的特性允許發送者(通稱 Alice)與接受者(通稱 Bob)能共同分享一組秘密且安全的鑰匙(secret key)。近年來,已有許多量子金鑰分配演算法被提出。
    我們結合了量子糾纏量(Quantum entanglement)與量子遠傳(Quantum teleportation)提出一個新穎的量子金鑰分配演算法。我們使用具有量子糾纏量子態(EPR pairs)來調變(modulate)我們的資訊,所以接受者(Bob)不需作選擇性的量測其所收到的量子態,因此大大提升產生金鑰的效率;再者,我們使用對稱控制反向電路(Bilateral CNOT)於兩組調變後的量子糾纏態,經由傳統通訊(classical communication)的協助與量子遠傳的保密性,我們加強了整個演算法的安全性與其對抗惡意侵犯者(通稱 Eve)的攻擊。然而,我們需要較多的資源: 具有量子糾纏態的量子態(Bell state)與具有量子糾纏態的量測裝置。
    最後,我們討論其安全性(Security)並與其他量子金鑰分配方法做比較。發現我們的方法在效率上優於其他的量子金鑰分配方法,於其他特性也都有不錯的表現。另外對於惡意者(Eve)的攻擊,我們有很好的抵抗力。然而,我們必須提防Eve想出更有效率的攻擊方式。


    Quantum teleportation allows an unknown quantum state to be
    transmitted from one place to another with the aid of
    classical communication by first preparing an EPR pair for the sender and the receiver.
    We propose a novel quantum key distribution protocol based on this idea. This protocol does not require the sender and the receiver to choose between alternative measurements, which improves the rate of generating key bits from the transmitted bits and is hard for an eavesdropper to access information. However, our
    scheme needs reliable Bell operator measurements and the
    expensive resource, two Bell states each round. The security of our schemes discussed and compared with others.

    Contents Abstract i Contents i List of Figures iv List of Tables vi 1 Introduction 1 2 Background 3 2.1 Basic Concepts of Quantum Computation . . . . . . . . . . . . . . . . . . . 3 2.2 Basic quantum operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Controlled operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Quantum Entanglement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3.1 Bell states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Entanglement Swapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 Quantum Teleportation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Quantum key distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6.1 The BB84 quantum key distribution . . . . . . . . . . . . . . . . . . 11 2.6.2 Quantum key distribution without alternative measurements . . . . . 12 3 Our Algorithm 15 3.1 Quantum key distribution with teleportation . . . . . . . . . . . . . . . . . . 15 3.1.1 Alice modulates EPR pair with her message . . . . . . . . . . . . . . 16 3.1.2 Bilateral XOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.1.3 Teleportation and transmission . . . . . . . . . . . . . . . . . . . . . 19 3.1.4 Bob analyzes his received message . . . . . . . . . . . . . . . . . . . . 22 3.1.5 A test for detecting eavesdropping . . . . . . . . . . . . . . . . . . . . 23 3.1.6 Summary of the protocol . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Security of the protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4 Comparison 29 5 Conclusion 35 A 36 A.1 Proof of no-cloning theorem [18] . . . . . . . . . . . . . . . . . . . . . . . . 36 A.2 Proof of information gain implying disturbance [18] . . . . . . . . . . . . . . 37 B 38 C Partial Trace 39 Bibliography 41

    [1] C. H. Bennett and G. Brassard, \Public-key distribution and coin tossing," in Proceed-
    ings of the IEEE International Conference on Computers, Systems, and Signal Process-
    ing, pp. 175{179, (1984).
    [2] A. K. Ekert, \Quantum cryptography based on bell's theorem," Phys. Rev. Lett., vol. 67,
    no. 6, pp. 661{663, (1991).
    [3] C. H. Bennett, \Quantum cryptography using any two nonorthogonal states," Phys.
    Rev. Lett., vol. 68, no. 21, pp. 3121{3124, (1992).
    [4] C. H. Bennett, G. Brassard, and N. D. Mermin, \Quantum cryptography without bell's
    theorem," Phys. Rev. Lett., vol. 68, no. 5, pp. 557{559, (1992).
    [5] L. Goldenberg and L. Vaidman, \Quantum cryptography based on orthogonal states,"
    Phys. Rev. Lett., vol. 75, no. 7, pp. 1239{1243, (1995).
    [6] B. Huttner, N. Imoto, N. Gisin, and T. Mor, \Quantum cryptography with coherent
    states," Phys. Rev. A, vol. 51, no. 3, pp. 1863{1869, (1995).
    [7] M. Koashi and N. Imoto, \Quantum cryptography based on split transmission of one-bit
    information in two steps," Phys. Rev. Lett., vol. 79, no. 12, pp. 2383{2386, (1997).
    [8] M. Ardehali, H. F. Chau, and H.-K. Lo, \E±cient quantum key distribution." quant-
    ph/9803007, (1999).
    [9] G. L. Long and X. S. Liu, \Theoretically e±cient high-capacity quantum-key-
    distribution scheme," Phys. Rev. A, vol. 65, pp. 032302(1){032302(3), (2002).
    [10] M. Zukowski, A. Zeilinger, and M. A. Horne, \Event-ready-detectors bell experiment
    via entanglement swapping," Phys. Rev. Lett., vol. 71, no. 26, pp. 4287{4290, (1993).
    [11] A. Cabello, \Quantum key distribution without alternative measurements," Phys. Rev.
    A, vol. 61, pp. 052312(1){052312(4), (2000).
    [12] Y. S. Zhang, C. F. Li, and G. C. Guo, \Comment on quantum key distribution without
    alternative measurements," Phys. Rev. A, vol. 63, pp. 036301(1){036301(2), (2001).
    [13] A. Cabello, \Addendum to quantum key distribution without alternative measure-
    ments," Phys. Rev. A, vol. 64, pp. 024301(1){024301(3), (2001).
    [14] C. H. Bennet, G. Brassard, C. Crepeau, R. Jozsa, A. Pere, and W. K. Wootters, \Tele-
    porting an unknown quantum state via dual classical and einstein-podolsky-rosen chan-
    nels," Phys. Rev. Lett., vol. 70, no. 13, pp. 1895{1899, (1993).
    [15] A. K. Ekert, B. Huttner, G. M. N. Palma, and A. Peres, \Eavesdropping on quantum-
    cryptographical systems," Phys. Rev. A, vol. 50, no. 2, pp. 1047{1056, (1994).
    [16] H. Bechmann-Pasquinucci, \Eavesdropping without quantum memory," arXiv:quant-
    ph/0504003, (2005).
    [17] S. L. Braunstein, A. Mann, and M. Revzen, \Maximal violation of bell inequalities for
    mixed states," Phys. Rev. Lett, vol. 68, no. 22, pp. 3259{3261, (1992).
    [18] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. the
    press syndicate of the university of cambridge, (2000).
    [19] C. H. Bennett, D. P. DiVincenzo, J. A. Amolin, and W. K. Wootters, \Mixed-state
    entanglement and quantum error correction," Phys. Rev. A, vol. 54, no. 5, pp. 3824{
    3851, (1996).
    [20] A. Zeilinger, M. A. Horne, H. Weinfurter, and M. Zukowski, \Three-particle entan-
    glements from two entangled pairs," Phys. Rev. Lett., vol. 78, no. 16, pp. 3031{3034,
    (1997).
    [21] S. Bose, V. Vedral, and P. L. Knight, \Multiparticle generalization of entanglement
    swapping," Phys. Rev. A, vol. 57, no. 2, pp. 822{829, (1998).
    [22] V. Karimipour, A. Bahraminasab, and S. Bagherinezhad, \Entanglement swapping
    of generalized cat states and secret sharing," Phys. Rev. A, vol. 65, pp. 042320(1){
    042320(5), (2002).
    [23] A. Cabello, \Quantum key distribution in the holevo limit," Phys. Rev. Lett., vol. 85,
    no. 26, pp. 5635{5638, (2000).

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