簡易檢索 / 詳目顯示

研究生: 邱靖益
Chiu, Ching-Yi
論文名稱: 量子可操控性偵測與量子密碼學
Detection of Quantum Steering and Its Application to Quantum Cryptography
指導教授: 李哲明
Li, Che-Ming
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 115
中文關鍵詞: 量子可操控性量子資訊理論量子竊聽量子密碼
外文關鍵詞: Quantum steering, Quantum information, Quantum eavesdropping, Quantum cryptography
相關次數: 點閱:142下載:5
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • Einstein-Podolsky-Rosen(EPR)可操控性描述了對於一個量子系統進行測量可以製備另一個系統狀態的性質,其起源於Schrödinger對於Einstein等人探討量子力學理論完備性之Einstein-Podolsky-Rosen悖論研究的回覆。本論文提出一個關於單系統可操控性的新穎概念,不同於兩個系統的EPR可操控性,其描述了傳送者量測系統並將其傳遞予接收者時,傳送者所進行的量測能製備接收者收到之系統狀態。我們設計了能夠偵測系統是否具此性質的實驗方案,並描述不具有可操控性的情境用以推導量子目擊;並證明當系統具有此性質時,我們可傳遞此系統完成安全密鑰分配,此外,我們亦說明如何將單系統量子目擊應用於偵測EPR可操控性。

    We propose a new concept of steering for single quantum d-dimensional systems and devise novel quantum witnesses to detect steerability which are applicable for both single-system steering and Einstein-Podolsky-Rosen (EPR) steering. These witnesses are useful to quantum communications for securing channels against both cloning-based individual attack and coherent attacks. It may be interesting to investigate further the steering transfer in quantum cloning machine.
    Key words: Quantum steering, Quantum information, Quantum eavesdropping, Quantum cryptography.

    目錄 中文摘要 I Abstract II 致謝 VIII 圖表目錄 XI 符號說明 XII 第一章 緒論 1 1.1 研究背景 1 1.2 研究動機 4 1.3 研究目的 5 1.4 論文架構 5 第二章 量子力學與四大公設 7 2.1 狀態向量 7 2.2 狀態的演化 8 2.3 量子系統的測量 10 2.4 複合系統 11 2.5 密度算符 13 2.6 開放量子系統 16 2.7 貝爾不等式與局域實在性 19 2.8 EPR 量子可操控性 22 第三章 古典資訊理論與量子資訊理論 27 3.1 古典資訊理論與夏農信息熵 27 3.2 量子資訊理論 30 3.2.1 量子信息熵與馮紐曼熵 31 3.2.2 信息熵的不確定性原理 34 3.2.3量子通訊與Holevo 邊界 35 第四章 量子密鑰分配與量子複製 40 4.1 BB84協議 41 4.2 E91協議 43 4.3 量子不可複製原理 44 4.4 包立量子複製 45 4.5 個別竊聽、集體竊聽與同調性竊聽 49 4.6 多維度量子系統密鑰分配對於個別竊聽之安全性 52 4.7 多維度系統秘鑰分配對於同調性與集體攻擊的安全性 58 第五章 單系統量子可操控性 65 5.1 時態性可操控性方案 65 5.2 單系統量子可操控性方案 71 5.2.1 可操控性的喪失與實在性系統之描述 73 5.2.2 可操控性偵測與量子目擊 78 5.2.2.1 條件機率可操控性量子目擊 79 5.2.2.2 信息熵可操控性量子目擊 81 5.2.3 可操控性量子目擊與量子秘鑰安全性 83 5.2.4 量子目擊的強健度 86 5.2.5 量子目擊與EPR可操控性 88 5.2.6 時態性可操控性不等式證明與不具可操控性系統描述 94 5.2.7 單系統量子目擊與時態性可操控性不等式比較 96 5.3 量子目擊的特性 99 第六章 驗證實驗 101 6.1 多維度貝爾不等式 101 6.2 多維度光子系統貝爾不等式驗證實驗設置與其應用於量子目擊 103 第七章 結論與未來展望 107 7.1 結論 107 7.2 未來展望 108 參考文獻 111

    [1] K. Helge, Quantum Generations: A History of Physics in the Twentieth Century Reprint. Princeton University Press, 2002.
    [2] D. Deutsch and A. Ekert, "Quantum computation," Physics World, vol. 11, pp. 47-52, 1998.
    [3] R. P. Feynman, "Simulating Physics with Computers," International Journal of Theoretical Physics, vol. 21, pp. 467-488, 1982.
    [4] C. H. Bennett and P. W. Shor, "Quantum information theory," Information Theory, IEEE Transactions on, vol. 44, pp. 2724-2742, 1998.
    [5] V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum metrology," Physical Review Letters, vol. 96, p. 4, 2006.
    [6] C. Branciard, E. G. Cavalcanti, S. P. Walborn, V. Scarani, and H. M. Wiseman, "One-sided device-independent quantum key distribution: Security, feasibility, and the connection with steering," Physical Review A, vol. 85, p. 010301, 2012.
    [7] Y.-N. Chen, C.-M. Li, N. Lambert, S.-L. Chen, Y. Ota, G.-Y. Chen, et al., "Temporal steering inequality," Physical Review A, vol. 89, p. 032112, 2014.
    [8] M. Vujicic and F. Herbut, "Distant steering: Schrodinger's version of quantum non-separability," Journal of Physics A: Mathematical and GeneralEmail alert RSS feed, vol. 21, p. 2913.
    [9] H. M. Wiseman, S. J. Jones, and A. C. Doherty, "Steering, Entanglement, Nonlocality, and the Einstein-Podolsky-Rosen Paradox," Physical Review Letters, vol. 98, p. 140402, 2007.
    [10] E. G. Cavalcanti, S. J. Jones, H. M. Wiseman, and M. D. Reid, "Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox," Physical Review A, vol. 80, p. 032112, 2009.
    [11] D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. J. Pryde, "Experimental EPR-steering using Bell-local states," Nat Phys, vol. 6, pp. 845-849, 2010.
    [12] B. Wittmann, S. Ramelow, F. Steinlechner, N. K. Langford, N. Brunner, H. M. Wiseman, et al., "Loophole-free Einstein–Podolsky–Rosen experiment via quantum steering," New Journal of Physics vol. 14, p. 053030, 2012.
    [13] D. H. Smith, G. Gillett, M. P. de Almeida, C. Branciard, A. Fedrizzi, T. J. Weinhold, et al., "Conclusive quantum steering with superconducting transition-edge sensors," Nature Communications, vol. 3, p. 625, 2012.
    [14] Q. Y. He and M. D. Reid, "Genuine Multipartite Einstein-Podolsky-Rosen Steering," Physical Review Letters, vol. 111, p. 250403, 2013.
    [15] S. Armstrong, M. Wang, R. Y. Teh, Q. Gong, Q. He, J. Janousek, et al., "Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks," Nature Physics, vol. 11, pp. 167-172, 2015.
    [16] D. Cavalcanti, P. Skrzypczyk, G. H. Aguilar, R. V. Nery, P. H. S. Ribeiro, and S. P. Walborn, "Detecting multipartite entanglement with untrusted measurements in asymmetric quantum networks," arXiv:1412.7730, 2014.
    [17] C.-M. Li, K. Chen, Y.-N. Chen, Q. Zhang, Y.-A. Chen, and J.-W. Pan, "Genuine High-Order Einstein-Podolsky-Rosen Steering," arXiv:1501.01452, 2015.
    [18] C. H. Bennett and G. Brassard, "Quantum cryptography: Public key distribution and coin tossing," In Proceedings of the IEEE International Conference on Computers, Systems and Signal, vol. 175, pp. 175–179, 1984.
    [19] A. K. Ekert, "Quantum cryptography based on Bell's theorem," Physical Review Letters, vol. 67, pp. 661-663, 1991.
    [20] N. Cerf, "Information-Theoretic Aspects of Quantum Copying," in Quantum Computing and Quantum Communications. vol. 1509, 218-234, 1999.
    [21] N. J. Cerf, "Pauli Cloning of a Quantum Bit," Physical Review Letters, vol. 84, pp. 4497-4500, 2000.
    [22] C. A. Fuchs, N. Gisin, R. B. Griffiths, C.-S. Niu, and A. Peres, "Optimal eavesdropping in quantum cryptography. I. Information bound and optimal strategy," Physical Review A, vol. 56, pp. 1163-1172, 1997.
    [23] W. K. Wootters and W. H. Zurek, "A single quantum cannot be cloned," Nature, vol. 299, pp. 802-803, 1982.
    [24] V. Bužek and M. Hillery, "Quantum copying: Beyond the no-cloning theorem," Physical Review A, vol. 54, pp. 1844-1852, 1996.
    [25] I. Csiszár and J. Körner, "Broadcast Channels with Confidential Messages," Transaction information theory, vol. 24, p. 339, 1978.
    [26] H. Bechmann-Pasquinucci and N. Gisin, "Incoherent and coherent eavesdropping in the six-state protocol of quantum cryptography," Physical Review A, vol. 59, pp. 4238-4248, 1999.
    [27] C. H. Bennett, C. C. G. Brassard, and U. M. Maurer, "Generalized Privacy Amplification," IEEE International Symposium on Information Theory, 1994.
    [28] J. I. Cirac and N. Gisin, "Coherent Eavesdropping Strategies for the Four State Quantum Cryptography Protocol," Physical Letters A, vol. 299, pp. 1-7, 1997.
    [29] N. Lütkenhaus, "Estimates for practical quantum cryptography," Physical Review A, vol. 59, pp. 3301-3319, 1999.
    [30] N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, "Security of Quantum Key Distribution Using d-Level Systems," Physical Review Letters, vol. 88, p. 127902, 2002.
    [31] L. Sheridan and V. Scarani, "Security proof for quantum key distribution using qudit systems," Physical Review A, vol. 82, p. 030301, 2010.
    [32] M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information: Cambridge university press, 2010.
    [33] J. S. Bell, "On the Einstein Podolsky Rosen Paradox," Physics vol. 1, pp. 195-200, 1964.
    [34] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, 2002.
    [35] O. Gühne and G. Tóth, "Entanglement detection," Physics Reports, vol. 474, pp. 1-79, 2009.
    [36] K. Kraus, "States, effects, and operations: fundamental notions of quantum theory," Lectures in mathematical physics at the University of Texas at Austin, vol. 190, 1983.
    [37] A. Einstein, B. Podolsky, and N. Rosen, "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?," Physical Review, vol. 47, pp. 777-780, 1935.
    [38] J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, "Proposed Experiment to Test Local Hidden-Variable Theories," Physical Review Letters, vol. 23, pp. 880-884, 1969.
    [39] E. Schrödinger, "Probability relations between separated systems," Mathematical Proceedings of the Cambridge Philosophical Society, vol. 32, pp. 446-452, 1936.
    [40] R. W. Spekkens, "Evidence for the epistemic view of quantum states: A toy theory," Physical Review A, vol. 75, p. 032110, 2007.
    [41] F. Verstraete, K. U. Leuven, K. U. Leuven, and M. Fannes, "A Study Of Entanglement In Quantum Information Theory," 2002.
    [42] M. Vujicic and F. Herbut, "Distant steering: Schrodinger's version of quantum non-separability," Journal of Physics A: Mathematical and GeneralEmail alert RSS feed, vol. 21, p. 2931, 1983.
    [43] K. A. Kirkpatrick, "The Schrödinger-HJW Theorem," Foundations of Physics Letters, vol. 19, p. 95, 2006.
    [44] C. E. Shannon, "A mathematical theory of communication," Mobile Computing and Communications Review, vol. 5, pp. 3-55, 2001.
    [45] T. M. Cover and J. A. Thomas, Elements of Information Theory, 1991.
    [46] I. I. Hirschman, "A note on entropy," American Journal of Mathematics, vol. 79, pp. 177-183, 1957.
    [47] N. J. Cerf and C. Adami, "Accessible information in quantum measurement," arXiv:quant-ph/9611032, 1996.
    [48] M. Tomamichel and R. Renner, "Uncertainty Relation for Smooth Entropies," Physical Review Letters, vol. 106, p. 110506, 2011.
    [49] W. Heisenberg, "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik," Zeitschrift für Physik, vol. 43, pp. 172-198, 1927.
    [50] A. S. Holevo, "Bounds for the quantity of information transmitted by a quantum communication channel," Problems of Information Transmission, vol. 9, pp. 177-183, 1973.
    [51] M. Takeoka, H. Krovi, and S. Guha, "Achieving the Holevo capacity of a pure state classical-quantum channel via unambiguous state discrimination," in Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on, 2013, pp. 166-170.
    [52] V. Giovannetti, S. Lloyd, and L. Maccone, "Achieving the Holevo bound via sequential measurements," Physical Review A, vol. 85, p. 012302, 2012.
    [53] M. Bourennane, A. Karlsson, G. Björk, N. Gisin, and N. J. Cerf, "Quantum key distribution using multilevel encoding: security analysis," Journal of Physics A: Mathematical and General, vol. 35, p. 10065, 2002.
    [54] T. Durt, D. Kaszlikowski, J.-L. Chen, and L. C. Kwek, "Security of quantum key distributions with entangled qudits," Physical Review A, vol. 69, p. 032313, 2004.
    [55] V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, "The security of practical quantum key distribution," Reviews of Modern Physics, vol. 81, pp. 1301-1350, 2009.
    [56] Vapnyarskii, Encyclopedia of Mathematics, 2001.
    [57] A. Ferenczi and N. Lütkenhaus, "Symmetries in quantum key distribution and the connection between optimal attacks and optimal cloning," Physical Review A, vol. 85, p. 052310, 2012.
    [58] J. Mora, M. Garcia, x00F, V. oz, A. Ruiz-Alba, W. Amaya, et al., "Experimental demonstration of a novel configuration for BB84 frequency coded QKD," in Information Photonics (IP), 2011 ICO International Conference on, 2011, pp. 1-2.
    [59] S. Goyal, A. H. Ibrahim, F. S. Roux, and A. F. Thomas Konrad, "Experimental orbital angular momentum based quantum key distribution through turbulence," arXiv:1412.0788, 2014.
    [60] A. C. Dada, J. Leach, G. S. Buller, M. J. Padgett, and E. Andersson, "Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities," Nature Physics, vol. 7, pp. 677-680, 2011.
    [61] H.-P. Lo, C.-M. Li, A. Yabushita, Y.-N. Chen, C.-W. Luo, and T. Kobayashi, "Experimental Violation of Bell Inequalities for Systems of over 4000 Dimensions," arXiv:1501.06429, 2015.
    [62] D. Collins, N. Gisin, N. Linden, S. Massar, and S. Popescu, "Bell Inequalities for Arbitrarily High-Dimensional Systems," Physical Review Letters, vol. 88, p. 040404, 2002.
    [63] J. B. Pors, S. S. R. Oemrawsingh, A. Aiello, M. P. van Exter, E. R. Eliel, G. W. ’t Hooft, et al., "Shannon Dimensionality of Quantum Channels and Its Application to Photon Entanglement," Physical Review Letters, vol. 101, p. 120502, 2008.
    [64] D. Bruß, "Optimal Eavesdropping in Quantum Cryptography with Six States," Physical Review Letters, vol. 81, pp. 3018-3021, 1998.

    下載圖示 校內:立即公開
    校外:立即公開
    QR CODE