依據量子力學的描述，量子同調性可使該物理系統據有量子特性，例如量子疊加、量子糾纏、貝爾非局域性及量子衝突性。這些特性為量子計算與量子通訊等相關量子科技應用的核心; 除此之外，在探討因量子同調性所產生之量子關聯性的議題中，量子衝突性因具有量子糾纏所沒有的量子特性而被廣為討論。本論文先以過程的角度討論物理過程保存同調性的能力，並提出兩種的量化工具，量化了資訊傳輸上受噪音干擾的過程、IBM 量子電腦邏輯運算的過程以及細菌和植物中光合作用系統能量傳遞的過程; 再者，以三體資訊圖拓展量子衝突性至三體量子衝突性，展示該關連性應用於三體量子態之特性，並與其他多體量子關連性分析，探討其應用優勢;最後，基於同調性為量子關連性中不可或缺的因素，結合量子同調目擊與量子衝突性，提出明確且詳細的實驗方案實現量子衝突性目擊，漸少偵測量子衝突性實驗所需的量測資源，並模擬實驗上製備和量測的變動造成的影響。

According to the description of quantum mechanics, quantum coherence can make a physical system possesses quantum characteristic such as quantum superposition, quantum entanglement, Bell nonlocality and quantum discord. These quantum features are the coresof quantum technologies such as quantum computation and quantum communication. Whilein the discussion of quantum correlation produced by quantum coherence, quantum discordis well discussed for owning the quantum characteristics that can not be found in quantum entanglement. In this thesis, we investigate the ability of preserving coherence for physical processes in the viewpoint of process and proposes two approaches to quantify it. We quantify the process of qubit transmission disturbed by noise, the process of computation for the logics of IBM quantum computer and the process of the energy transport of photosynthesis in bacteria and plants. Furthermore, we extend the quantum discord to tripartite quantum discord by the concept of tripartite information diagram. The proposed quantum discord is demonstrated by tripartite quantum states. In addition, the connections between tripartite quantum discord and other quantum correlations are briefly discussed. Finally, due to that quantum coherence is an indispensable factor for quantum discord, we use the tool “witnessing quantum coherence” to achieve “witnessing quantum discord” and simulate possible experimental errors. By this way, it reduces the requirement of experimental resources for detecting quantum discord.

[1] A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?,” Physical Review, vol. 47, no. 10, p. 777, 1935.
[2] E. Schrödinger, “Discussion of probability relations between separated systems,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31, no. 4, p. 555–563, 1935.
[3] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox,” Physical Review Letters, vol. 98, no. 14, p. 140402, 2007.
[4] J. Bell, “On the Einstein-Podolsky-Rosen paradox,” Physics, vol. 1, no. RX-1376, pp. 195–200, 1964.
[5] H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Physical Review Letters, vol. 88, no. 1, p. 017901, 2001.
[6] L. Henderson and V. Vedral, “Classical, quantum and total correlations,” Journal of Physics A Mathematical General, vol. 34, pp. 6899–6905, 2001.
[7] R. P. Feynman, “Simulating physics with computers,” International Journal of Theoretical Physics, vol. 21, no. 6-7, pp. 467–488, 1982.
[8] D. Deutsch and A. Ekert, “Quantum computation,” Physics World, vol. 11, no. 3, p. 47, 1998.
[9] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, “Quantum computers,” Nature, vol. 464, no. 7285, p. 45, 2010.
[10] C. Bennett and P. Shor, “Quantum information theory,” IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2724–2742, 1998.
[11] V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Physical Review Letters, vol. 96, no. 1, p. 010401, 2006.
[12] E. M. Gauger, E. Rieper, J. J. Morton, S. C. Benjamin, and V. Vedral, “Sustained quantum coherence and entanglement in the avian compass,” Physical Review Letters, vol. 106, no. 4, p. 040503, 2011.
[13] N. Lambert, Y.-N. Chen, Y.-C. Cheng, C.-M. Li, G.-Y. Chen, and F. Nori, “Quantum biology,” Nature Physics, vol. 9, no. 1, p. 10, 2013.
[14] Y. Yao, X. Xiao, L. Ge, and C. Sun, “Quantum coherence in multipartite systems,” Physical Review A, vol. 92, no. 2, p. 022112, 2015.
[15] R. J. Glauber, “The quantum theory of optical coherence,” Physical Review, vol. 130, pp. 2529–2539, 1963.
[16] E. C. G. Sudarshan, “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams,” Physical Review Letters, vol. 10, pp. 277–279, 1963.
[17] L. Mandel and E. Wolf, “Coherence properties of optical fields,” Reviews of Modern Physics, vol. 37, pp. 231–287, 1965.
[18] T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Physical Review Letters, vol. 113, p. 140401, 2014.
[19] F. Levi and F. Mintert, “A quantitative theory of coherent delocalization,” New Journal of Physics, vol. 16, no. 3, p. 033007, 2014.
[20] M. Koashi and A. Winter, “Monogamy of quantum entanglement and other correlations,” Physical Review A, vol. 69, no. 2, p. 022309, 2004.
[21] F. Fanchini, L. Castelano, M. Cornelio, and M. De Oliveira, “Locally inaccessible information as a fundamental ingredient to quantum information,” New Journal of Physics, vol. 14, no. 1, p. 013027, 2012.
[22] C. Rulli and M. Sarandy, “Global quantum discord in multipartite systems,” Physical Review A, vol. 84, no. 4, p. 042109, 2011.
[23] I. Chakrabarty, P. Agrawal, and A. K. Pati, “Quantum dissension: Generalizing quantum discord for three-qubit states,” The European Physical Journal D, vol. 65, no. 3, pp. 605–612, 2011.
[24] J.-H. Hsieh, S.-H. Chen, and C.-M. Li, “Quantifying quantum-mechanical processes,” Scientific Reports, vol. 7, no. 1, p. 13588, 2017.
[25] J.-H. Hsieh, “Theory of quantifying quantum-mechanical processes and its applications,” Mater’s Thesis, 2017.
[26] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, 2010.
[27] International Business Machines Corporation, “IBM Q, The quantum computer.” http: //research.ibm.com/ibm-q/.
[28] G. S. Engel, T. R. Calhoun, E. L. Read, T.-K. Ahn, T. Mančal, Y.-C. Cheng, R. E. Blankenship, and G. R. Fleming, “Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems,” Nature, vol. 446, no. 7137, p. 782, 2007.
[29] A. Pais, “Einstein and the quantum theory,” Reviews of Modern Physics, vol. 51, no. 4, p. 863, 1979.
[30] R. Shankar, Principles of quantum mechanics. Springer Science & Business Media, 2012.
[31] K.-C. Toh, M. J. Todd, and R. H. Tütüncü, “SDPT3–A Matlab software package for semidefinite-quadratic-linear programming in Matlab®, version 4.0,” Handbook on Semidefinite, Conic and Polynomial Optimization, pp. 715–754, 2012.
[32] J. Löfberg, “YALMIP: a toolbox for modeling and optimization in MATLAB®,” in Computer Aided Control Systems Design, 2004 IEEE International Symposium on, pp. 284–289, IEEE, 2004.
[33] J. Adolphs and T. Renger, “How proteins trigger excitation energy transfer in the fmo complex of green sulfur bacteria,” Biophysical Journal, vol. 91, no. 8, pp. 2778–2797, 2006.
[34] J. M. Chow, A. D. Córcoles, J. M. Gambetta, C. Rigetti, B. R. Johnson, J. A. Smolin, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Simple all-microwave entangling gate for fixed-frequency superconducting qubits,” Physical Review Letters, vol. 107, p. 080502, 2011.
[35] M. B. Plenio and S. F. Huelga, “Dephasing-assisted transport: quantum networks and biomolecules,” New Journal of Physics, vol. 10, no. 11, p. 113019, 2008.
[36] F. Caruso, A. W. Chin, A. Datta, S. F. Huelga, and M. B. Plenio, “Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport,” The Journal of Chemical Physics, vol. 131, no. 10, p. 09B612, 2009.
[37] 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. 885, 2012.
[38] M. M. Wilde, J. M. McCracken, and A. Mizel, “Could light harvesting complexes exhibit non-classical effects at room temperature?,” in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 466, pp. 1347–1363, The Royal Society, 2010.
[39] M. Bourennane, M. Eibl, C. Kurtsiefer, S. Gaertner, H. Weinfurter, O. Gühne, P. Hyllus, D. Bruß, M. Lewenstein, and A. Sanpera, “Experimental detection of multipartite entanglement using witness operators,” Physical Review Letters, vol. 92, no. 8, p. 087902, 2004.
[40] C.-M. Li, K. Chen, Y.-N. Chen, Q. Zhang, Y.-A. Chen, and J.-W. Pan, “Genuine highorder Einstein-Podolsky-Rosen steering,” Physical Review Letters, vol. 115, no. 1, p. 010402, 2015.
[41] W.-T. Lee and C.-M. Li, “Revealing tripartite quantum discord with tripartite information diagram,” Entropy, vol. 19, no. 11, p. 602, 2017.
[42] T. M. Cover and J. A. Thomas, Elements of information theory. John Wiley & Sons, 2012.
[43] S. Ghahramani, Fundamentals of Probability: With Stochastic Processes. CRC Press, 2015.
[44] S. Luo, “Using measurement-induced disturbance to characterize correlations as classical or quantum,” Physical Review A, vol. 77, no. 2, p. 022301, 2008.
[45] N. Gisin and R. Thew, “Quantum communication,” Nature Photonics, vol. 1, no. 3, p. 165, 2007.
[46] 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, pp. 69–72, Springer, 1989.
[47] R. F. Werner, “Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model,” Physical Review A, vol. 40, no. 8, p. 4277, 1989.
[48] B. Dakić, V. Vedral, and Č. Brukner, “Necessary and sufficient condition for nonzero quantum discord,” Physical Review Letters, vol. 105, no. 19, p. 190502, 2010.
[49] A. Bera, T. Das, D. Sadhukhan, S. S. Roy, A. S. De, and U. Sen, “Quantum discord and its allies: a review of recent progress,” Reports on Progress in Physics, vol. 81, no. 2, p. 024001, 2017.
[50] Y. Shih, “Entangled biphoton source-property and preparation,” Reports on Progress in Physics, vol. 66, no. 6, p. 1009, 2003.
[51] H. Lu, C. Liu, D.-S. Wang, L.-K. Chen, Z.-D. Li, X.-C. Yao, L. Li, N.-L. Liu, C.-Z. Peng, B. C. Sanders, et al., “Experimental quantum channel simulation,” Physical Review A, vol. 95, no. 4, p. 042310, 2017.
[52] W.-T. Lee and C.-M. Li, “Revealing tripartite quantum discord with tripartite information diagram,” Entropy, vol. 19, no. 11, p. 602, 2017.
[53] C.-C. Kuo, “Quantum process capability and its applications,” Mater’s Thesis, 2018.
[54] W. Son, J. Lee, and M. Kim, “Generic Bell inequalities for multipartite arbitrary dimensional systems,” Physical Review Letters, vol. 96, no. 6, p. 060406, 2006.
[55] N. D. Mermin, “Extreme quantum entanglement in a superposition of macroscopically distinct states,” Physical Review Letters, vol. 65, pp. 1838–1840, 1990.
[56] M. Ardehali, “Bell inequalities with a magnitude of violation that grows exponentially with the number of particles,” Physical Review A, vol. 46, pp. 5375–5378, 1992.
[57] J. Lavoie, R. Kaltenbaek, and K. J. Resch, “Experimental violation of Svetlichny’s inequality,” New Journal of Physics, vol. 11, no. 7, p. 073051, 2009.
[58] G. Svetlichny, “Distinguishing three-body from two-body nonseparability by a Bell-type inequality,” Physical Review D, vol. 35, no. 10, p. 3066, 1987.
[59] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Physical Review A, vol. 64, p. 052312, 2001.