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系統識別號 U0026-2107201411130100
論文名稱(中文) 量子同調性質之偵測
論文名稱(英文) Detecting Quantum Coherence
校院名稱 成功大學
系所名稱(中) 工程科學系
系所名稱(英) Department of Engineering Science
學年度 102
學期 2
出版年 103
研究生(中文) 賴弘洋
研究生(英文) Hung-Yang Lai
學號 n96011538
學位類別 碩士
語文別 中文
論文頁數 120頁
口試委員 指導教授-李哲明
口試委員-廖德祿
口試委員-黃吉川
口試委員-陳岳男
中文關鍵字 量子同調性  量子目擊  量子衝突性  量子狀態轉移  量子資訊處理 
英文關鍵字 Quantum coherence  Quantum witness  Quantum discord  Quantum state transitions  Quantum information processing 
學科別分類
中文摘要 驗證系統的量子特性在量子科技的應用是十分關鍵的課題。根據量子力學的預測，系統在一個量子過程中，狀態間可以利用同調的方式互相轉移，這樣的轉移方式可以用來發展量子技術，例如量子元件與量子計算；此外，量子糾纏態的關聯性可以提供嶄新的資訊處理方式，這樣的關聯性可以透過量子衝突性來表示；上述量子特徵都是源自於量子系統的同調性質。本論文提出在實驗上可行及有效率的方式，偵測多體狀態的量子轉移過程與量子衝突性。這些建構在量子同調目擊上的偵測方式，提供實驗上有效率的方法用來偵測此兩者的量子特徵，並且可以廣泛應用在各種量子系統中，包括奈米結構中電荷的傳輸過程以及運算光學量子位元所需的多量子位元邏輯閘。比起目前量子性質的偵測方式，例如量子維度目擊、量子斷層掃描以及量子衝突性，我們提出的偵測方式可以減少實驗上所需的量測資源，並且可作為未來研究更複雜之量子系統與演化之基礎。
英文摘要 Quantum coherence is one of the main features of quantum system. It serves important resources for quantum science and technology, such as quantum computing, quantum metrology and quantum biology. In this thesis, we devise experimentally feasible and efficient methods to detect quantum discord and genuine quantum multi-state transitions. Experimental proposals for implementing these schemes are introduced as well in the end.
論文目次 中文摘要 I
Abstract II
致謝 IX
目錄 X
圖目錄 XIII
表目錄 XVII
符號說明 XVIII
第一章 緒論 1
1.1 研究背景 1
1.2 研究動機 3
1.3 研究目的 5
1.4 本文組織架構 6
第二章 量子力學與糾纏光源 7
2.1 狀態空間與狀態向量 7
2.2 密度算符 8
2.3 量子的運動方程式 10
2.4 量子系統的測量 12
2.5 複合系統與糾纏態 14
2.6 開放的量子系統 16
2.7 主方程式 17
2.7.1 馬可夫演化 17
2.7.2 李維空間與主方程式 18
2.8 糾纏光源 21
第三章 量子的同調性偵測 23
3.1 貝爾不等式 23
3.2 萊格特-皋格不等式 25
3.3 量子斷層掃描 27
3.4 維度目擊 32
3.5 量子目擊 34
第四章 多體狀態轉移的偵測 36
4.1 多體狀態轉移模擬架構 36
4.2 傅立葉轉換 41
4.3 一般量子系統 42
4.3.1 簡併能級 43
4.3.2 非簡併能級 48
4.3.3 耗散系統 49
4.4 包含古典混合的量子系統 51
4.4.1 初始態為純態 53
4.4.2 初始態為疊加態 59
4.5 量子位元的耦合 60
4.5.1 2個量子位元耦合 61
4.5.2 3個量子位元耦合 69
4.6 模擬實例 72
4.6.1 庫柏對 72
4.6.2 量子點 73
4.6.3 拉比震盪 75
第五章 量子衝突性偵測 77
5.1 古典資訊理論 77
5.2 量子資訊理論 79
5.3 量子衝突性 80
5.4 量子衝突性偵測 83
第六章 驗證實驗 88
6.1 光學設備介紹 88
6.2 符合計數器 91
6.2.1 符合計數 91
6.2.2 布林邏輯運算 93
6.2.3 符合計數器 94
6.3 糾纏光源 97
6.4 多體狀態轉移偵測 106
6.5 量子衝突性偵測 109
第七章 結論與未來展望 111
7.1 結論 111
7.2 未來展望 112
参考文獻 113
參考文獻 [1] D. Deutsch and A. Ekert, "Quantum computation," Physics World, vol. 11, pp. 47-52, Mar 1998.
[2] R. P. Feynman, "Simulating physics with computers," International Journal of Theoretical Physics, vol. 21, pp. 467-488, 1982.
[3] C. H. Bennett and P. W. Shor, "Quantum information theory," Ieee Transactions on Information Theory, vol. 44, pp. 2724-2742, Oct 1998.
[4] V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum metrology," Physical Review Letters, vol. 96, p. 4, Jan 2006.
[5] E. Schrödinger, What is Life?: Cambridge Univ. Press, 1992.
[6] A. J. Leggett and A. Garg, "Quantum-mechanics versus macroscopic realism - is the flux there when nobody looks," Physical Review Letters, vol. 54, pp. 857-860, 1985.
[7] J. Bell, "On the Einstein Podolsky Rosen Paradox," Physics 1, vol. 3, pp. 195-200, 1964.
[8] A. Aspect, J. Dalibard, and G. Roger, "Experimental test of bell inequalities using time-varying analyzers," Physical Review Letters, vol. 49, pp. 1804-1807, 1982.
[9] M. F. Bocko and R. Onofrio, "On the measurement of a weak classical force coupled to a harmonic oscillator: Experimental progress," Reviews of Modern Physics, vol. 68, pp. 755-799, Jul 1996.
[10] C. M. Caves, K. S. Thorne, R. W. P. Drever, V. D. Sandberg, and M. Zimmermann, "On the measurement of a weak classical force coupled to a quantum-mechanical oscillator .1. issues of principle," Reviews of Modern Physics, vol. 52, pp. 341-392, 1980.
[11] Y. Aharonov and L. Vaidman, "Properties of a quantum system during the time interval between 2 measurements," Physical Review A, vol. 41, pp. 11-20, Jan 1990.
[12] G. C. Knee, S. Simmons, E. M. Gauger, J. J. L. Morton, H. Riemann, N. V. Abrosimov, et al., "Violation of a Leggett-Garg inequality with ideal non-invasive measurements," Nature Communications, vol. 3, p. 6, Jan 2012.
[13] O. Guhne and G. Toth, "Entanglement detection," Physics Reports-Review Section of Physics Letters, vol. 474, pp. 1-75, Apr 2009.
[14] M. E. Goggin, M. P. Almeida, M. Barbieri, B. P. Lanyon, J. L. O'Brien, A. G. White, et al., "Violation of the Leggett-Garg inequality with weak measurements of photons," Proceedings of the National Academy of Sciences of the United States of America, vol. 108, pp. 1256-1261, Jan 2011.
[15] V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum-enhanced measurements: Beating the standard quantum limit," Science, vol. 306, pp. 1330-1336, Nov 2004.
[16] A. Palacios-Laloy, F. Mallet, F. Nguyen, P. Bertet, D. Vion, D. Esteve, et al., "Experimental violation of a Bell's inequality in time with weak measurement," Nature Physics, vol. 6, pp. 442-447, Jun 2010.
[17] S. F. Huelga, T. W. Marshall, and E. Santos, "Proposed test for realist theories using rydberg atoms coupled to a high-q resonator," Physical Review A, vol. 52, pp. R2497-R2500, Oct 1995.
[18] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, "Quantum entanglement," Reviews of Modern Physics, vol. 81, pp. 865-942, Apr-Jun 2009.
[19] R. Gallego, N. Brunner, C. Hadley, and A. Acin, "Device-Independent Tests of Classical and Quantum Dimensions," Physical Review Letters, vol. 105, pp. 230501 (4 pp.)-230501 (4 pp.), 3 2010.
[20] N. Brunner, M. Navascues, and T. Vertesi, "Dimension Witnesses and Quantum State Discrimination," Physical Review Letters, vol. 110, Apr 2013.
[21] C. M. Li, N. Lambert, Y. N. Chen, G. Y. Chen, and F. Nori, "Witnessing Quantum Coherence: from solid-state to biological systems," Scientific Reports, vol. 2, p. 9, Nov 2012.
[22] A. Ishizaki and Y. Tanimura, "Quantum dynamics of system strongly coupled to low-temperature colored noise bath: Reduced hierarchy equations approach," Journal of the Physical Society of Japan, vol. 74, pp. 3131-3134, Dec 2005.
[23] A. P. Alivisatos, "Semiconductor clusters, nanocrystals, and quantum dots," Science, vol. 271, pp. 933-937, Feb 1996.
[24] G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mancal, Y. C. Cheng, et al., "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems," Nature, vol. 446, pp. 782-786, Apr 2007.
[25] E. Collini, C. Y. Wong, K. E. Wilk, P. M. Curmi, P. Brumer, and G. D. Scholes, "Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature," Nature, vol. 463, pp. 644-7, Feb 4 2010.
[26] J. Yuen-Zhou, J. J. Krich, M. Mohseni, and A. Aspuru-Guzik, "Quantum state and process tomography of energy transfer systems via ultrafast spectroscopy," Proceedings of the National Academy of Sciences, vol. 108, pp. 17615-17620, 2011.
[27] D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, "Bell theorem without inequalities," American Journal of Physics, vol. 58, pp. 1131-1143, Dec 1990.
[28] N. Gisin and H. Bechmann-Pasquinucci, "Bell inequality, Bell states and maximally entangled states for n qubits," Physics Letters A, vol. 246, pp. 1-6, Sep 1998.
[29] O. Guhne, P. Hyllus, D. Bruss, A. Ekert, M. Lewenstein, C. Macchiavello, et al., "Detection of entanglement with few local measurements," Physical Review A, vol. 66, p. 5, Dec 2002.
[30] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, "Quantum entanglement," Reviews of Modern Physics, vol. 81, p. 865, 2009.
[31] G. Toth and O. Guhne, "Detecting genuine multipartite entanglement with two local measurements," Physical Review Letters, vol. 94, p. 4, Feb 2005.
[32] Y. C. Cheng and G. R. Fleming, "Dynamics of Light Harvesting in Photosynthesis," in Annual Review of Physical Chemistry. vol. 60, ed Palo Alto: Annual Reviews, 2009, pp. 241-262.
[33] J. Ahrens, P. Badziag, A. Cabello, and M. Bourennane, "Experimental device-independent tests of classical and quantum dimensions," Nature Physics, vol. 8, pp. 592-595, Aug 2012.
[34] M. Hendrych, R. Gallego, M. Micuda, N. Brunner, A. Acin, and J. P. Torres, "Experimental estimation of the dimension of classical and quantum systems," Nature Physics, vol. 8, pp. 588-591, Aug 2012.
[35] A. Acin, N. Brunner, N. Gisin, S. Massar, S. Pironio, and V. Scarani, "Device-independent security of quantum cryptography against collective attacks," Physical Review Letters, vol. 98, p. 4, Jun 2007.
[36] H. Ollivier and W. H. Zurek, "Quantum discord: A measure of the quantumness of correlations," Physical Review Letters, vol. 88, p. 4, Jan 2002.
[37] M. Gessner and H.-P. Breuer, "Local witness for bipartite quantum discord," Physical Review A, vol. 87, p. 042107, 2013.
[38] K. Blum, Density matrix theory and applications vol. 64: Springer, 2012.
[39] H. J. Carmichael, Statistical methods in quantum optics vol. 2: Springer, 1999.
[40] M. A. Nielsen and I. L. Chuang, Quantum computation and quantum information: Cambridge university press, 2010.
[41] D. J. Griffiths, Introduction to quantum mechanics: pearson new international edition: Pearson Education Limited, 2013.
[42] O. Gühne and G. Tóth, "Entanglement detection," Physics Reports, vol. 474, pp. 1-75, 2009.
[43] D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Going beyond Bell’s theorem," in Bell’s theorem, quantum theory and conceptions of the universe, ed: Springer, 1989, pp. 69-72.
[44] H. J. Briegel and R. Raussendorf, "Persistent entanglement in arrays of interacting particles," Physical Review Letters, vol. 86, p. 910, 2001.
[45] K. Chen, C.-M. Li, Q. Zhang, Y.-A. Chen, A. Goebel, S. Chen, et al., "Experimental realization of one-way quantum computing with two-photon four-qubit cluster states," Physical review letters, vol. 99, p. 120503, 2007.
[46] P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter, V. Vedral, et al., "Experimental one-way quantum computing," Nature, vol. 434, pp. 169-176, Mar 2005.
[47] J. Preskill, "Lecture notes for physics 229: Quantum information and computation," California Institute of Technology, 1998.
[48] Y.-A. Chen, S. Chen, Z.-S. Yuan, B. Zhao, C.-S. Chuu, J. Schmiedmayer, et al., "Memory-built-in quantum teleportation with photonic and atomic qubits," Nature Physics, vol. 4, pp. 103-107, 2008.
[49] C.-W. Chou, H. De Riedmatten, D. Felinto, S. Polyakov, S. Van Enk, and H. J. Kimble, "Measurement-induced entanglement for excitation stored in remote atomic ensembles," Nature, vol. 438, pp. 828-832, 2005.
[50] D. Leibfried, E. Knill, S. Seidelin, J. Britton, R. B. Blakestad, J. Chiaverini, et al., "Creation of a six-atom ‘Schrödinger cat’state," Nature, vol. 438, pp. 639-642, 2005.
[51] H. Häffner, W. Hänsel, C. Roos, J. Benhelm, M. Chwalla, T. Körber, et al., "Scalable multiparticle entanglement of trapped ions," Nature, vol. 438, pp. 643-646, 2005.
[52] T. Yamamoto, Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J.-S. Tsai, "Demonstration of conditional gate operation using superconducting charge qubits," Nature, vol. 425, pp. 941-944, 2003.
[53] Y. A. Pashkin, T. Yamamoto, O. Astafiev, Y. Nakamura, D. Averin, and J. Tsai, "Quantum oscillations in two coupled charge qubits," Nature, vol. 421, pp. 823-826, 2003.
[54] I. Chiorescu, Y. Nakamura, C. M. Harmans, and J. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science, vol. 299, pp. 1869-1871, 2003.
[55] 黃衍介, 近代實驗光學: 臺灣東華, 2005.
[56] A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Physical review, vol. 47, p. 777, 1935.
[57] A. Garg, "Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?," Physical Review Letters, 1985.
[58] N. Lambert, C. Emary, Y.-N. Chen, and F. Nori, "Distinguishing quantum and classical transport through nanostructures," Physical review letters, vol. 105, p. 176801, 2010.
[59] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, "Measurement of qubits," Physical Review A, vol. 64, p. 15, Nov 2001.
[60] S. M. Tan, "A quantum optics toolbox for Matlab 5," J. Opt. B: Quantum Semiclass. Opt, vol. 1, p. 161, 1999.
[61] K. Modi, T. Paterek, W. Son, V. Vedral, and M. Williamson, "Unified View of Quantum and Classical Correlations," Physical Review Letters, vol. 104, p. 4, Feb 2010.
[62] A. Miranowicz, M. Bartkowiak, X. G. Wang, Y. X. Liu, and F. Nori, "Testing nonclassicality in multimode fields: A unified derivation of classical inequalities," Physical Review A, vol. 82, p. 14, Jul 2010.
[63] M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J. M. Raimond, et al., "Quantum rabi oscillation: A direct test of field quantization in a cavity," Physical Review Letters, vol. 76, pp. 1800-1803, Mar 1996.
[64] E. T. Jaynes, "Information theory and statistical mechanics," Physical review, vol. 106, p. 620, 1957.
[65] C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature, vol. 404, pp. 247-255, 2000.
[66] R. F. Werner, "Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model," Physical Review A, vol. 40, pp. 4277-4281, 1989.
[67] P. Kok, "Quantum optics: Entangled photons report for duty," Nature Photonics, vol. 4, pp. 504-505, 2010.
[68] G. Boole, "The calculus of logic," Cambridge and Dublin Mathematical Journal, vol. 3, pp. 183-198, 1848.
[69] Y. Shih, "Entangled biphoton source-property and preparation," Reports on Progress in Physics, vol. 66, p. 1009, 2003.
[70] Y. H. Shih and A. V. Sergienko, "2-photon anti-correlation in a Hanbury Brown-Twiss type experiment," Physics Letters A, vol. 186, pp. 29-34, Mar 1994.
[71] Y. H. Shih and A. V. Sergienko, "Observation of quantum beating in a simple beam-splitting experiment - 2-particle entanglement in spin and space-time," Physical Review A, vol. 50, pp. 2564-2568, Sep 1994.
[72] M. Fox, Quantum Optics: An Introduction: An Introduction vol. 15: Oxford University Press, 2006.
[73] D. J. Saunders, S. J. Jones, H. M. Wiseman, and G. Pryde, "Experimental EPR-steering using Bell-local states," Nature Physics, vol. 6, pp. 845-849, 2010.
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