臺灣博碩士論文加值系統

探討隨時間演化的Kossakowski矩陣的積範數的負值與BLP、LFS、RHP、糾纏、量子不和諧(Quantum Discord)以及伴正定演算法(SDP)的非馬可夫測度的關係。在BLP、LFS及SDP測度，量子位元對與環境耦合強度的比愈大，非馬可夫性在歐姆性為縱軸與相對相位為橫軸的平面上，可探測到的非馬可夫性分布較廣，但高峰值下降。而基於動力學半群理論以及量子動力學過程是否具有可分性的 Kossakowski 矩陣測度和 RHP 測度，量子位元對與環境耦合強度有正比關係。而量子不和諧測度得出的結果，與我們使用的其他測度所量測出的非馬可夫性的趨勢不相似，與量子位元對與環境耦合強度沒有正比關係且歐姆環境模數s<2量測不到非馬可夫性，也與[Sci. Rep. 11, 10046 (2021)]所說有所不同的，當歐姆環境模數s<2觀測不到非馬可夫性。最後，基於正偏轉置（PPT）準則的糾纏測量結果對於維度高於量子位元對的情況來說不夠強。

The relationship between the negative value of the trace norm of the time evolving Kossakowski matrix and the non-Markovianity measures of the BLP, LFS, RHP, entanglement, quantum discord, and the SDP (semidefinite program) measured are discussed. In the BLP, LFS, and SDP measurements, the ratio of the coupling strength of the qubit pair to the environment is larger. The non-Markovianity distribution is wider, but the high peak drops on the plane, where the ohmicity is the vertical axis and the relative phase is the horizontal axis. Based on the theory of dynamical semigroups and whether the quantum dynamic process is divisibility for the Kossakowski matrix measure and the RHP measure, they are proportional to the ratio of the coupling strength between the qubit pair and the environment; in contrast, the quantum discord measures do not show such behavior. Moreover, the latter two measures can even capture the non-Markovianity when the Ohmicities less than 2, which is typically considered to be Markovian as shown in existing literature [Sci. Rep. 11, 10046 (2021) 1]. Finally, the results of the entanglement measure based on positive partial transpose (PPT) criterion are not strong enough for the case of dimension higher than qubit pair.

ABSTRACT I
摘要 II
ACKNOWLEDGEMENT III
誌謝 IV
Contents V
List of Figures VII
Chapter I Introduction 1
Chapter Ⅱ Open Quantum System Dynamics 3
Chapter Ⅲ Presentation and Meaning of Math 6
Ⅰ. Completely Positivity and Trace-Preserving (CPTP) 6
Ⅱ. Dynamical maps Λ 7
Ⅲ. Dynamical Semigroup 7
Ⅳ. Divisibility 8
Ⅴ. Representation of the dynamical map 8
Chapter Ⅳ Non-Markovianity Measures 10
Ⅰ. Master equation and Kossakowski matrix 10
Ⅱ. BLP Measure 11
Ⅲ. LFS Measure 12
Ⅳ. RHP Measure 13
Ⅴ. Entanglement 14
Ⅵ. Quantum Discord 15
Ⅶ. SDP 17
Chapter Ⅴ Qubit Pair Pure Dephasing Model 19
Ⅰ. Our Model 19
Ⅱ. Apply Measures 22
II Ⅰ. Kossakowski Measure 22
II Ⅱ. BLP Measure 25
II Ⅲ. LFS Measure 28
II Ⅳ. RHP Measure 29
II Ⅴ. Entanglement Measure 32
II Ⅵ. Quantum Discord Measure 33
II Ⅶ. SDP Measure 35
Chapter Ⅵ Numerical Results 37
Chapter Ⅶ Conclusion 43
REFERENCE 44

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