簡易檢索 / 詳目顯示

回結果列表
研究生： 高祐謙
Kao, Yu-Chien
論文名稱： 識別實驗量子力學過程：從光子非馬可夫動力學到遠程量子態之非古典準備
Identification of Experimental Quantum-Mechanical Processes: from Photonic Non-Markovian Dynamics to Nonclassical Preparation of Quantum Remote States
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： 2020
畢業學年度： 108
語文別： 英文
論文頁數： 132
中文關鍵詞： 量子過程 、光子非馬可夫動力學 、遠程狀態之準備
外文關鍵詞： Quantum process, Photonic non-Markovian dynamics, Remote state preparation
相關次數： 點閱：101  下載：1 
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

    • 量子力學過程在量子資訊處理裡扮演了關鍵的角色，例如：量子計算中量子位元的動力學和量子邏輯運算，量子通訊中遠程狀態之準備，這些都可以視為過程的問題，因此在實驗上精準的識別量子力學過程就顯得至關重要。其中，有兩個重要的識別量子過程之課題：第一，系統與環境之間的交互作用：馬可夫與非馬可夫動力學過程；第二，任務導向的量子資訊處理之過程是否能超越古典動力學過程的描述？本論文第一部分，我們提供了對於非局域動力學更精準的識別；我們仔細評估現有文獻的實驗數據，證明了非局域動力學無法發生在該實驗之物理情境下，我們展現了量化量子過程為基礎的非馬可夫量度，對於辨識非馬可夫動力學有更好的解析度，這有利於需要精確分辨非馬可夫動力學之應用，例如：在容錯量子計算中，馬可夫與非馬可夫假設下的誤差模型，所估算出的誤差門檻值有所不同，所以實驗上應該先精準判斷量子位元的動力學，再檢驗該量子計算是否能達到相對之誤差門檻值。第二部分，我們理論和實驗上探討了遠程量子態之準備過程，是否能超越藉由古典動力學準備遠程狀態之過程；我們認為量子過程操縱性 (quantum process steering)，才是完成遠程狀態之非古典準備的一種資源；實驗上，我們透過偏振糾纏光子對來實現遠程狀態之非古典準備，展現了如何量化量子過程操縱性以及古典與量子準備遠程狀態之間的轉換，這能讓我們識別一個實驗的遠程狀態之準備是否為一個遠程狀態之非古典準備。以上兩種方法提供了對於實驗量子過程精確的辨識，這有助於提升判斷量子力學效應以及其在量子技術上之應用之精確性。

    Quantum-mechanical processes play a crucial role in quantum-information processing, such as identifying the dynamics of qubits and quantum logic operations in quantum computation and performing remote state preparation (RSP) in quantum communication. Therefore, accurate methods for identifying quantum-mechanical processes are essential in implementing practical quantum information and quantum computation systems. In developing such methods, two issues are of particular importance, namely (1) the nature of the interaction between the system of interest and the environment (i.e., Markovian or non-Markovian dynamical processes); and (2) whether or not the task-oriented processes in quantum-information processing go beyond the mimicry of classical dynamical processes. The first part of this thesis thus provides a precise identification criterion for nonlocal dynamics. Based on a careful examination of the experimental data in the existing literature, it is shown that nonlocal dynamics cannot occur in existing physical scenarios. Moreover, the proposed criterion has a finer resolution in identifying non-Markovian dynamics than the conventional trace distance criterion. It is thus beneficial in facilitating the precise process classifications required by certain quantum-enhanced applications. For example, in fault-tolerant quantum computation, estimating the error threshold depends strongly on the underlying assumption of the error model (i.e., Markovian or non-Markovian). Accordingly, it is necessary to identify the dynamics of the qubits before examining the quantum computation with the resulting error threshold. The second part of the thesis conducts a theoretical and experimental investigation into the question as to whether RSP can outperform classical dynamical processes when preparing remote states. It is shown that quantum process steering is a necessary resource for performing nonclassical RSP. It is further shown that quantum process steering can be measured by realizing nonclassical RSP which employs polarization-correlated photon pairs. Finally, the transition from classical to quantum RSP by controlling the quantum process steering resource is demonstrated experimentally using a variety of polarization-correlated photon pairs. The results provide a practical means of identifying truly quantum RSP. Overall, the formalism proposed in this thesis facilitates the accurate identification of experimental quantum-mechanical processes and is thus of significant benefit in enhancing the identification accuracy of quantum-mechanical effects and their applications in quantum technology.

    摘要 i Abstract ii 誌謝 iv Table of Contents vi List of Tables x List of Figures xi Nomenclature xii Chapter 1. Introduction 1 1.1. Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. General concept of open quantum systems . . . . . . . . . . . . . . . . . 2 1.1.2. General concept of remote state preparation . . . . . . . . . . . . . . . 3 1.2. Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1. Identification of non-Markovian dynamics . . . . . . . . . . . . . . 4 1.2.2. Necessary resource for achieving quantum RSP from quantum theory perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 1.3. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1. Identification of nonlocal memory effects from process analysis perspective . .7 1.3.2. Necessary resource for achieving nonclassical RSP from classical dynamical process perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Chapter 2. Description of Quantum-Mechanical Processes 12 2.1. Quantum operation formalism . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2. Quantum tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1. Quantum state tomography . . . . . . . . . . . . . . . . . . . . . . 14 2.2.2. Quantum process tomography . . . . . . . . . . . . . . . . . . . . 15 Chapter 3. Absence of Evidence for Nonlocal Dynamics in Open Quantum Systems 19 3.1. System dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1.1. Description of local dynamics and global dynamics . . . . . . . . . 20 3.1.2. Definition of nonlocal dynamics in open quantum system . . . . . . 22 3.2. Previous theoretical study of nonlocal dynamics and related experiment . . 23 3.2.1. Photonic experiment on nonlocal dynamics . . . . . . . . . . . . . 23 3.2.2. Generic decoherence process . . . . . . . . . . . . . . . . . . . . . 26 3.2.3. The BLP non-Markovian criterion . . . . . . . . . . . . . . . . . . 27 3.2.4. Conclusion of the previous studies . . . . . . . . . . . . . . . . . . 28 3.3. Identifying nonlocal dynamics by examining quantum-mechanical process . 30 3.3.1. The robustness non-Markovian criterion . . . . . . . . . . . . . . . 30 3.3.2. Construction of the experimental process matrix . . . . . . . . . . . 33 3.3.3. Identifying non-Markovianity by the robustness non-Markovian criterion . .37 3.4. Comparisons with previous studies and discussions of nonlocal dynamics . 42 3.4.1. Comparisons of the identification of nonlocal dynamics with previous studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.4.2. Related applications in quantum-information processing . . . . . . 45 Chapter 4. Nonclassical Preparation of Quantum Remote States 47 4.1. Remote state preparation protocol . . . . . . . . . . . . . . . . . . . . . . 48 4.2. Theory of quantum process steering . . . . . . . . . . . . . . . . . . . . . 49 4.3. Methods of identifying and quantifying quantum process steering . . . . . . 52 4.4. Experiment and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.4.1. Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4.2. Experimental results . . . . . . . . . . . . . . . . . . . . . . . . 57 Chapter 5. Summary and Outlook 61 5.1. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.2.1. Non-markovian effects in fault-tolerant quantum computation . . . 63 5.2.2. Device-independent remote state preparation . . . . . . . . . . . . 66 References 68 Appendix A. Semi-definite programming 76 Appendix B. The paper to be submitted for publication 79 Appendix C. Comparisons between the generalized LHS model and the standard LHS model 91 Appendix D. Quantum composition, quantum robustness, and the fidelity criteria 95 Appendix E. Experimental photon pairs 100 Appendix F. Noise model for experimental photon pairs 102 Appendix G. Compensation of the photon walk-off effect 104 Appendix H. Implementation of RSP protocol and resulting theoretical prediction of the process steerability 109 Appendix I. Quantum discord and EPR steerability of the created photon pairs 112 I.1. Geometric discord, steerable weight, and steering robustness . . . . . . . . 112 I.1.1. Geometric discord . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 I.1.2. Steerable weight . . . . . . . . . . . . . . . . . . 114 I.1.3. Steering robustness . . . . . . . . . . . . . . . . . 114 Appendix J. The paper to be submitted for publication 116

    [1] J. P. Dowling and G. J. Milburn, “Quantum technology: the second quantum revolution,” Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 361, no. 1809, pp. 1655–1674, 2003.
    [2] J.L.O’brien, A.Furusawa, andJ.Vučković, “Photonicquantumtechnologies,” Nature Photonics, vol. 3, no. 12, p. 687, 2009.
    [3] D. Deutsch and A. Ekert, “Quantum computation,” Physics World, vol. 11, no. 3, p. 47, 1998.
    [4] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O＇Brien, “Quantum computers,” Nature, vol. 464, no. 7285, pp. 45–53, 2010.
    [5] N. Gisin and R. Thew, “Quantum communication,” Nature Photonics, vol. 1, no. 3, pp. 165–171, 2007.
    [6] V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum metrology,” Physical Review Letters, vol. 96, no. 1, p. 010401, 2006.
    [7] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Reviews of modern physics, vol. 74, no. 1, p. 145, 2002.
    [8] K. Kraus, A. Böhm, J. D. Dollard, and W. Wootters, “States, effects, and operations: fundamental notions of quantum theory. lectures in mathematical physics at the university of texas at austin,” Lecture Notes in Physics, vol. 190, 1983.
    [9] H.­P. Breuer, F. Petruccione, et al., The theory of open quantum systems. Oxford University Press on Demand, 2002.
    [10] R. P. Feynman and F. Vernon Jr, “The theory of a general quantum system interacting with a linear dissipative system,” Annals of Physics, vol. 24, pp. 118–173, 1963.
    [11] F. Shibata, Y. Takahashi, and N. Hashitsume, “A generalized stochastic liouville equation. non­markovian versus memoryless master equations,” Journal of Statistical Physics, vol. 17, no. 4, pp. 171–187, 1977.
    [12] G. Gasbarri and L. Ferialdi, “Recursive approach for non­markovian timeconvolutionless master equations,” Physical Review A, vol. 97, no. 2, p. 022114, 2018.
    [13] I. De Vega and D. Alonso, “Dynamics of non­markovian open quantum systems,” Reviews of Modern Physics, vol. 89, no. 1, p. 015001, 2017.
    [14] Y.­N. Chen, G.­Y. Chen, Y.­Y. Liao, N. Lambert, and F. Nori, “Detecting nonmarkovian plasmonic band gaps in quantum dots using electron transport,” Physical Review B, vol. 79, no. 24, p. 245312, 2009.
    [15] W.­M. Zhang, P.­Y. Lo, H.­N. Xiong, M. W.­Y. Tu, and F. Nori, “General nonmarkovian dynamics of open quantum systems,” Physical Review Letters, vol. 109, no. 17, p. 170402, 2012.
    [16] X. Yin, J. Ma, X. Wang, and F. Nori, “Spin squeezing under non­markovian channels by the hierarchy equation method,” Physical Review A, vol. 86, no. 1, p. 012308, 2012.
    [17] D. Chruściński and S. Maniscalco, “Degree of non­markovianity of quantum evolution,” Physical Review Letters, vol. 112, no. 12, p. 120404, 2014.
    [18] H.­B. Chen, J.­Y. Lien, G.­Y. Chen, and Y.­N. Chen, “Hierarchy of non­markovianity and k­divisibility phase diagram of quantum processes in open systems,” Physical Review A, vol. 92, no. 4, p. 042105, 2015.
    [19] H.­B. Chen, N. Lambert, Y.­C. Cheng, Y.­N. Chen, and F. Nori, “Using non­markovian measures to evaluate quantum master equations for photosynthesis,” Scientific Reports, vol. 5, no. 1, pp. 1–12, 2015.
    [20] H.­N. Xiong, P.­Y. Lo, W.­M. Zhang, F. Nori, et al., “Non­markovian complexity in the quantum­to­classical transition,” Scientific Reports, vol. 5, p. 13353, 2015.
    [21] D. F. Urrego, J. Flórez, J. Svozilík, M. Nuñez, and A. Valencia, “Controlling nonmarkovian dynamics using a light­based structured environment,” Physical Review A, vol. 98, no. 5, p. 053862, 2018.
    [22] H.­P. Breuer, E.­M. Laine, J. Piilo, and B. Vacchini, “Colloquium: Non­markovian dynamics in open quantum systems,” Reviews of Modern Physics, vol. 88, no. 2, p. 021002, 2016.
    [23] H.­P. Breuer, “Foundations and measures of quantum non­markovianity,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 45, no. 15, p. 154001, 2012.
    [24] Á. Rivas, S. F. Huelga, and M. B. Plenio, “Quantum non­markovianity: characterization, quantification and detection,” Reports on Progress in Physics, vol. 77, no. 9, p. 094001, 2014.
    [25] H.­P. Breuer, E.­M. Laine, and J. Piilo, “Measure for the degree of non­markovian behavior of quantum processes in open systems,” Physical Review Letters, vol. 103, no. 21, p. 210401, 2009.
    [26] E.­M. Laine, J. Piilo, and H.­P. Breuer, “Measure for the non­markovianity of quantum processes,” Physical Review A, vol. 81, no. 6, p. 062115, 2010.
    [27] S.­L. Chen, N. Lambert, C.­M. Li, A. Miranowicz, Y.­N. Chen, and F. Nori, “Quantifying non­markovianity with temporal steering,” Physical Review Letters, vol. 116, no. 2, p. 020503, 2016.
    [28] Á. Rivas, S. F. Huelga, and M. B. Plenio, “Entanglement and non­markovianity of quantum evolutions,” Physical Review Letters, vol. 105, no. 5, p. 050403, 2010.
    [29] S. Luo, S. Fu, and H. Song, “Quantifying non­markovianity via correlations,” Physical Review A, vol. 86, no. 4, p. 044101, 2012.
    [30] K.­D. Wu, Z. Hou, G.­Y. Xiang, C.­F. Li, G.­C. Guo, D. Dong, and F. Nori, “Detecting non­markovianity via quantified coherence: theory and experiments,” npj Quantum Information, vol. 6, no. 1, pp. 1–7, 2020.
    [31] C. H. Bennett, D. P. DiVincenzo, P. W. Shor, J. A. Smolin, B. M. Terhal, and
    W. K. Wootters, “Remote state preparation,” Physical Review Letters, vol. 87, no. 7,
    p. 077902, 2001.
    [32] A. K. Pati, “Minimum classical bit for remote preparation and measurement of a qubit,” Physical Review A, vol. 63, no. 1, p. 014302, 2000.
    [33] C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein­podolsky­rosen channels,” Physical Review Letters, vol. 70, no. 13, p. 1895, 1993.
    [34] S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, and S. L. Braunstein, “Advances in quantum teleportation,” Nature Photonics, vol. 9, no. 10, p. 641, 2015.
    [35] E. Jeffrey, N. A. Peters, and P. G. Kwiat, “Towards a periodic deterministic source of arbitrary single­photon states,” New Journal of Physics, vol. 6, no. 1, p. 100, 2004.
    [36] J. T. Barreiro, T.­C. Wei, and P. G. Kwiat, “Remote preparation of single­photon“hybrid＂entangled and vector­polarization states,” Physical Review Letters, vol. 105, no. 3, p. 030407, 2010.
    [37] W. Rosenfeld, S. Berner, J. Volz, M. Weber, and H. Weinfurter, “Remote preparation of an atomic quantum memory,” Physical Review Letters, vol. 98, no. 5, p. 050504, 2007.
    [38] X.­H. Bao, X.­F. Xu, C.­M. Li, Z.­S. Yuan, C.­Y. Lu, and J.­W. Pan, “Quantum teleportation between remote atomic­ensemble quantum memories,” Proceedings of the National Academy of Sciences, vol. 109, no. 50, pp. 20347–20351, 2012.
    [39] B. Dakić, Y. O. Lipp, X. Ma, M. Ringbauer, S. Kropatschek, S. Barz, T. Paterek, V. Vedral, A. Zeilinger, Č. Brukner, et al., “Quantum discord as resource for remote state preparation,” Nature Physics, vol. 8, no. 9, pp. 666–670, 2012.
    [40] E.­M. Laine, H.­P. Breuer, J. Piilo, C.­F. Li, and G.­C. Guo, “Nonlocal memory effects in the dynamics of open quantum systems,” Physical Review Letters, vol. 108, no. 21, p. 210402, 2012.
    [41] K. H. Hughes, C. D. Christ, and I. Burghardt, “Effective­mode representation of nonmarkovian dynamics: A hierarchical approximation of the spectral density. i. application to single surface dynamics,” The Journal of chemical physics, vol. 131, no. 2, p. 024109, 2009.
    [42] P. Siegle, I. Goychuk, P. Talkner, and P. Hänggi, “Markovian embedding of nonmarkovian superdiffusion,” Physical Review E, vol. 81, no. 1, p. 011136, 2010.
    [43] R. Martinazzo, B. Vacchini, K. H. Hughes, and I. Burghardt, “Communication: Universal markovian reduction of brownian particle dynamics,” The Journal of Chemical Physics, vol. 134, no. 1, p. 011101, 2011.
    [44] M. Woods, R. Groux, A. Chin, S. F. Huelga, and M. B. Plenio, “Mappings of open quantum systems onto chain representations and markovian embeddings,” Journal of Mathematical Physics, vol. 55, no. 3, p. 032101, 2014.
    [45] B.­H. Liu, D.­Y. Cao, Y.­F. Huang, C.­F. Li, G.­C. Guo, E.­M. Laine, H.­P. Breuer, and J. Piilo, “Photonic realization of nonlocal memory effects and non­markovian quantum probes,” Scientific Reports, vol. 3, no. 1, pp. 1–6, 2013.
    [46] 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.
    [47] W. H. Zurek, “Einselection and decoherence from an information theory perspective,” Annalen der Physik, vol. 9, no. 11­12, pp. 855–864, 2000.
    [48] L. Henderson and V. Vedral, “Classical, quantum and total correlations,” Journal of Physics A: Mathematical and General, vol. 34, no. 35, p. 6899, 2001.
    [49] 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.
    [50] S. Luo and S. Fu, “Geometric measure of quantum discord,” Physical Review A, vol. 82, no. 3, p. 034302, 2010.
    [51] N. Killoran, D. N. Biggerstaff, R. Kaltenbaek, K. J. Resch, and N. Lütkenhaus, “Derivation and experimental test of fidelity benchmarks for remote preparation of arbitrary qubit states,” Physical Review A, vol. 81, no. 1, p. 012334, 2010.
    [52] H. M. Wiseman, S. J. Jones, and A. C. Doherty, “Steering, entanglement, nonlocality, and the einstein­podolsky­rosen paradox,” Physical Review Letters, vol. 98, no. 14, p. 140402, 2007.
    [53] M. Reid, P. Drummond, W. Bowen, E. G. Cavalcanti, P. K. Lam, H. Bachor, U. L. Andersen, and G. Leuchs, “Colloquium: the einstein­podolsky­rosen paradox: from concepts to applications,” Reviews of Modern Physics, vol. 81, no. 4, p. 1727, 2009.
    [54] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information. Cambridge University Press, 2000.
    [55] P. G. Kwiat, A. J. Berglund, J. B. Altepeter, and A. G. White, “Experimental verification of decoherence­free subspaces,” Science, vol. 290, no. 5491, pp. 498–501, 2000.
    [56] J.­S. Xu, X.­Y. Xu, C.­F. Li, C.­J. Zhang, X.­B. Zou, and G.­C. Guo, “Experimental investigation of classical and quantum correlations under decoherence,” Nature Communications, vol. 1, no. 1, pp. 1–6, 2010.
    [57] E.­M. Laine, H.­P. Breuer, J. Piilo, C.­F. Li, and G.­C. Guo, “Erratum: Nonlocal memory effects in the dynamics of open quantum systems [phys. rev. lett. 108, 210402 (2012)],” Physical Review Letters, vol. 111, no. 22, p. 229901, 2013.
    [58] S. Wißmann and H.­P. Breuer, “Nonlocal quantum memory effects in a correlated multimode field,” arXiv preprint arXiv:1310.7722, 2013.
    [59] S. Wißmann and H.­P. Breuer, “Role of entanglement for nonlocal memory effects,” Physical Review A, vol. 90, no. 3, p. 032117, 2014.
    [60] V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, “Completely positive dynamical semigroups of n­level systems,” Journal of Mathematical Physics, vol. 17, no. 5, pp. 821–825, 1976.
    [61] G. Lindblad, “On the generators of quantum dynamical semigroups,” Communications in Mathematical Physics, vol. 48, no. 2, pp. 119–130, 1976.
    [62] J.­H. Hsieh, S.­H. Chen, and C.­M. Li, “Quantifying quantum­mechanical processes,” Scientific Reports, vol. 7, no. 1, pp. 1–13, 2017.
    [63] N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of Modern Physics, vol. 86, no. 2, p. 419, 2014.
    [64] 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.
    [65] K.­C. Toh, M. J. Todd, and R. H. Tütüncü, “SDPT3–A Matlab software package for semidefinite­quadratic­linear programming in Matlab®, version 4.0,” Handbook on Semidefinite, Conic and Polynomial Optimization, pp. 715–754, 2012.
    [66] K.­H. Wang, S.­H. Chen, Y.­C. Lin, and C.­M. Li, “Non­markovianity of photon dynamics in a birefringent crystal,” Physical Review A, vol. 98, no. 4, p. 043850, 2018.
    [67] E.­M. Laine, H.­P. Breuer, and J. Piilo, “Nonlocal memory effects allow perfect teleportation with mixed states,” Scientific Reports, vol. 4, p. 4620, 2014.
    [68] Z.­D. Liu, Y.­N. Sun, B.­H. Liu, C.­F. Li, G.­C. Guo, S. H. Raja, H. Lyyra, and J. Piilo, “Experimental realization of high­fidelity teleportation via non­markovian open quantum system,” arXiv:2007.01318, 2020.
    [69] B.­H. Liu, X.­M. Hu, Y.­F. Huang, C.­F. Li, G.­C. Guo, A. Karlsson, E.­M. Laine, S. Maniscalco, C. Macchiavello, and J. Piilo, “Efficient superdense coding in the presence of non­markovian noise,” Europhysics Letters, vol. 114, no. 1, p. 10005, 2016.
    [70] A. Cabello, “N­particle n­level singlet states: some properties and applications,” Physical Review Letters, vol. 89, no. 10, p. 100402, 2002.
    [71] Y.­N. Chen, C.­M. Li, N. Lambert, S.­L. Chen, Y. Ota, G.­Y. Chen, and F. Nori, “Temporal steering inequality,” Physical Review A, vol. 89, no. 3, p. 032112, 2014.
    [72] S.­L. Chen, N. Lambert, C.­M. Li, A. Miranowicz, Y.­N. Chen, and F. Nori, “Quantifying non­markovianity with temporal steering,” Physical Review Letters, vol. 116, no. 2, p. 020503, 2016.
    [73] P. Skrzypczyk, M. Navascués, and D. Cavalcanti, “Quantifying einstein­podolskyrosen steering,” Physical Review Letters, vol. 112, no. 18, p. 180404, 2014.
    [74] M. Piani and J. Watrous, “Necessary and sufficient quantum information characterization of einstein­podolsky­rosen steering,” Physical Review Letters, vol. 114, no. 6, p. 060404, 2015.
    [75] H. F. Hofmann, “Complementary classical fidelities as an efficient criterion for the evaluation of experimentally realized quantum operations,” Physical Review Letters, vol. 94, no. 16, p. 160504, 2005.
    [76] P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zeilinger, A. V. Sergienko, and Y. Shih, “New high­intensity source of polarization­entangled photon pairs,” Physical Review Letters, vol. 75, no. 24, p. 4337, 1995.
    [77] J. Lavoie, R. Kaltenbaek, M. Piani, and K. J. Resch, “Experimental bound entanglement in a four­photon state,” Physical Review Letters, vol. 105, no. 13, p. 130501, 2010.
    [78] E. Amselem and M. Bourennane, “Experimental four­qubit bound entanglement,” Nature Physics, vol. 5, no. 10, pp. 748–752, 2009.
    [79] P. Shor, “Proceedings of the 37th annual symposium on foundations of computer science,” 1996.
    [80] D. Aharonov and M. Ben­Or, “Fault­tolerant quantum computation with constant error rate,” SIAM Journal on Computing, 2008.
    [81] A. Y. Kitaev, “Fault­tolerant quantum computation by anyons,” Annals of Physics, vol. 303, no. 1, pp. 2–30, 2003.
    [82] E. Knill, R. Laflamme, and W. H. Zurek, “Resilient quantum computation,” Science, vol. 279, no. 5349, pp. 342–345, 1998.
    [83] D. Gottesman, “Theory of fault­tolerant quantum computation,” Physical Review A, vol. 57, no. 1, p. 127, 1998.
    [84] R. Raussendorf and H. J. Briegel, “A one­way quantum computer,” Physical Review Letters, vol. 86, no. 22, p. 5188, 2001.
    [85] H. J. Briegel, D. E. Browne, W. Dür, R. Raussendorf, and M. Van den Nest, “Measurement­based quantum computation,” Nature Physics, vol. 5, no. 1, pp. 19– 26, 2009.
    [86] K. S. Chou, J. Z. Blumoff, C. S. Wang, P. C. Reinhold, C. J. Axline, Y. Y. Gao, L. Frunzio, M. Devoret, L. Jiang, and R. Schoelkopf, “Deterministic teleportation of a quantum gate between two logical qubits,” Nature, vol. 561, no. 7723, pp. 368–373, 2018.
    [87] A. Pirker, J. Wallnöfer, and W. Dür, “Modular architectures for quantum networks,” New Journal of Physics, vol. 20, no. 5, p. 053054, 2018.
    [88] K. Beyer, K. Luoma, and W. T. Strunz, “Steering heat engines: A truly quantum maxwell demon,” Physical Review Letters, vol. 123, p. 250606, 2019.
    [89] E. T. Campbell, B. M. Terhal, and C. Vuillot, “Roads towards fault­tolerant universal quantum computation,” Nature, vol. 549, no. 7671, pp. 172–179, 2017.
    [90] D. A. Lidar and T. A. Brun, Quantum error correction. Cambridge university press, 2013.
    [91] P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Physical Review A, vol. 52, no. 4, p. R2493, 1995.
    [92] A. M. Steane, “Error correcting codes in quantum theory,” Physical Review Letters, vol. 77, no. 5, p. 793, 1996.
    [93] D. Gottesman, “Stabilizer codes and quantum error correction,” arXiv preprint quantph/9705052, 1997.
    [94] D. Aharonov and M. Ben­Or, “Proceedings of the 29th annual acm symposium on theory of computing,” 1997.
    [95] A. Y. Kitaev, “Quantum computations: algorithms and error correction,” Russian Mathematical Surveys, vol. 52, no. 6, p. 1191, 1997.
    [96] E. Knill, R. Laflamme, and W. H. Zurek, “Resilient quantum computation: error models and thresholds,” Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, vol. 454, no. 1969, pp. 365–384, 1998.
    [97] P. Aliferis, D. Gottesman, and J. Preskill, “Quantum accuracy threshold for concatenated distance­3 codes,” arXiv preprint quant­ph/0504218, 2005.
    [98] B. W. Reichardt, “Fault­tolerance threshold for a distance­three quantum code,” in International Colloquium on Automata, Languages, and Programming, pp. 50–61, Springer, 2006.
    [99] A. M. Steane, “Overhead and noise threshold of fault­tolerant quantum error correction,” Physical Review A, vol. 68, no. 4, p. 042322, 2003.
    [100] W. Dür and H.­J. Briegel, “Entanglement purification for quantum computation,” Physical Review Letters, vol. 90, no. 6, p. 067901, 2003.
    [101] B. M. Terhal and G. Burkard, “Fault­tolerant quantum computation for local nonmarkovian noise,” Physical Review A, vol. 71, no. 1, p. 012336, 2005.
    [102] D. Aharonov, A. Kitaev, and J. Preskill, “Fault­tolerant quantum computation with long­range correlated noise,” Physical Review Letters, vol. 96, no. 5, p. 050504, 2006.
    [103] E. Knill, “Quantum computing with realistically noisy devices,” Nature, vol. 434, no. 7029, pp. 39–44, 2005.
    [104] M. Steffen, M. Ansmann, R. C. Bialczak, N. Katz, E. Lucero, R. McDermott, M. Neeley, E. M. Weig, A. N. Cleland, and J. M. Martinis, “Measurement of the entanglement of two superconducting qubits via state tomography,” Science, vol. 313, no. 5792, pp. 1423–1425, 2006.
    [105] G. Ithier, E. Collin, P. Joyez, P. Meeson, D. Vion, D. Esteve, F. Chiarello, A. Shnirman, Y. Makhlin, J. Schriefl, et al., “Decoherence in a superconducting quantum bit circuit,” Physical Review B, vol. 72, no. 13, p. 134519, 2005.
    [106] J. Schreier, A. A. Houck, J. Koch, D. I. Schuster, B. Johnson, J. Chow, J. M. Gambetta, J. Majer, L. Frunzio, M. H. Devoret, et al., “Suppressing charge noise decoherence in superconducting charge qubits,” Physical Review B, vol. 77, no. 18, p. 180502, 2008.
    [107] R. Barends, J. Kelly, A. Megrant, A. Veitia, D. Sank, E. Jeffrey, T. C. White, J. Mutus, A. G. Fowler, B. Campbell, et al., “Superconducting quantum circuits at the surface code threshold for fault tolerance,” Nature, vol. 508, no. 7497, pp. 500–503, 2014.
    [108] J. M. Chow, J. M. Gambetta, E. Magesan, D. W. Abraham, A. W. Cross, B. Johnson, N. A. Masluk, C. A. Ryan, J. A. Smolin, S. J. Srinivasan, et al., “Implementing a strand of a scalable fault­tolerant quantum computing fabric,” Nature Communications, vol. 5, no. 1, pp. 1–9, 2014.
    [109] J. Benhelm, G. Kirchmair, C. F. Roos, and R. Blatt, “Towards fault­tolerant quantum computing with trapped ions,” Nature Physics, vol. 4, no. 6, pp. 463–466, 2008.
    [110] T. Choi, S. Debnath, T. Manning, C. Figgatt, Z.­X. Gong, L.­M. Duan, and C. Monroe, “Optimal quantum control of multimode couplings between trapped ion qubits for scalable entanglement,” Physical Review Letters, vol. 112, no. 19, p. 190502, 2014.
    [111] J. Morris, F. A. Pollock, and K. Modi, “Non­markovian memory in ibmqx4,” arXiv preprint arXiv:1902.07980, 2019.
    [112] J. Helsen, F. Battistel, and B. M. Terhal, “Spectral quantum tomography,” NPJ Quantum Information, vol. 5, no. 1, pp. 1–11, 2019.
    [113] L. Vandenberghe and S. Boyd, “Semidefinite programming,” SIAM Review, vol. 38, no. 1, pp. 49–95, 1996.
    [114] S.Boyd, S.P.Boyd, andL.Vandenberghe, Convexoptimization. Cambridgeuniversity press, 2004.
    [115] A. Gilchrist, N. K. Langford, and M. A. Nielsen, “Distance measures to compare real and ideal quantum processes,” Physical Review A, vol. 71, no. 6, p. 062310, 2005.
    [116] J. Lofberg, “Yalmip: A toolbox for modeling and optimization in matlab,” in 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508), pp. 284–289, IEEE, 2004.
    [117] K.­C. Toh, R. Tütüncü, and M. Todd, “On the implementation and usage of sdpt3–a matlab software package for semidefinite­quadratic­linear programming, version 4.0,” Handbook on Semidefinite, Conic and Polynomial Optimization, vol. 166, 01 2012.
    [118] I. L. Chuang and M. A. Nielsen, “Prescription for experimental determination of the dynamics of a quantum black box,” Journal of Modern Optics, vol. 44, no. 11­12, pp. 2455–2467, 1997.
    [119] D. F. V. James, P. G. Kwiat, W. J. Munro, and A. G. White, “Measurement of qubits,” Physical Review A, vol. 64, p. 052312, Oct 2001.
    [120] M. H. Rubin, D. N. Klyshko, Y. Shih, and A. Sergienko, “Theory of two­photon entanglement in type­ii optical parametric down­conversion,” Physical Review A, vol. 50, no. 6, p. 5122, 1994.
    [121] S. M. Lee, H. Kim, M. Cha, and H. S. Moon, “Polarization­entangled photon­pair source obtained via type­ii non­collinear spdc process with ppktp crystal,” Optics Express, vol. 24, no. 3, pp. 2941–2953, 2016.

    下載圖示 校內：2025-07-16公開
    校外：2025-07-16公開
    QR CODE