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系統識別號 U0026-0801201322234800
論文名稱(中文) 雙分系統糾纏參數的研究
論文名稱(英文) A study of entanglement measures in bipartite systems
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 101
學期 1
出版年 102
研究生(中文) 陳奕翔
研究生(英文) Yi-Hsiang Chen
學號 l26004022
學位類別 碩士
語文別 英文
論文頁數 39頁
口試委員 指導教授-許祖斌
口試委員-周忠憲
口試委員-楊緒濃
中文關鍵字 高維度  糾纏參數  二乘三系統 
英文關鍵字 higher dimensional  entanglement parameters  qubit-qutrit system 
學科別分類
中文摘要 在更高維度的純態雙分系統裡我們展示了糾纏的精細描述。除了二乘二系
統以外,我們需要一個以上的參數來描述糾纏。一個系統非糾纏性的充分必要
條件是所有的糾纏參數都為零的狀況,每個糾纏參數都可視為一個二乘二系統
的糾纏。這邊將探討這些糾纏參數的各種性質,而且重點放在二乘三的系統,
此種系統是需要多於一個糾纏參數的最簡單的系統。其中探討了糾纏參數的對
稱性、可交換與非交換Hopf纖維化和糾纏參數的精確對應、糾纏參數的測
量,最後提供明確的物理系統來展示這些糾纏參數的表現行為。
英文摘要 Finer characterizations of entanglement have been shown to exist in higher dimensional pure bipartite systems. Beyond qubit-qubit systems, more than one parameter is necessary to capture the entanglement. The necessary and suffi cient condition for separability is equivalent to the vanishing of a set of entanglement parameters, each of which can be associated with a qubit-qubit entanglement. Properties of these entanglement parameters are investigated, and attention is focussed on the qubit-qutrit system-the simplest system which requires more than one parameter of entanglement.Symmetries in the entanglement parameters, and the precise parametrization of entanglement in Abelian and non-Abelian Hopf brations of the Hilbert space are also
discussed. Measurement of the entanglement parameters is also addressed, and explicit physical examples are used to verify and exemplify the behavior of the entanglement parameters.
論文目次 Contents
1 Introduction and overview ... 3
2 A brief review of ner entanglement parameters for pure bipartite systems ... 4
3 Symmetries of entanglements ... 5
3.1 Entanglements symmetry on 2 by m system ... 5
3.2 Symmetry on total entanglement of n by m state ... 6
4 Finer characterizations of entanglement parameters: Explicit examples ... 10
4.1 6-state Hopf bration and entanglement ... 10
4.2 Abelian Hopf bration ... 11
4.3 Non-abelian quaternionic Hopf bration ... 12
5 Measurement of entanglement parameters ... 15
6 Entanglement of spin-spin interaction: 4 and 6-state examples ... 20
7 Example of 6-state decomposition from total spin state to bipartite qubit-qutrit system ... 24
7.1 Rotating magnetic eld couple with two spin ... 24
7.2 Clebsch-Gordan division into bipartite state ... 28
7.3 Calculation on entanglement parameters ... 30
7.4 Time dependence of the entanglement parameters ... 31
8 Concluding remarks ... 38
References ... 39
參考文獻 [1] E. Schrodinger, Discussion of Probability Relations between Separated Systems, Proceedings
of the Cambridge Philosophical Society 31, 555-563, (1935).
[2] Che-Shu Lee, Finer Characterizations of Pure Bipartite Entanglement, M. Sc. thesis,
Dept. of Physics, National Cheng Kung University (2012).
[3] Huei-Chen Lin, A study of the geometric phase in quantum mechanics, M. Sc. thesis,
Dept. of Physics, National Cheng Kung University (2009).
[4] Jung-Bin Wang, Non-abelian Geometric Phase and Quaternionic Hopf Fibration,
M. Sc. thesis, Dept. of Physics, National Cheng Kung University (2011).
[5] Kai-Siang Neo, A study of the Clauser-Horne-Shimony-Holt relation, M. Sc. thesis,
Dept. of Physics, National Cheng Kung University (2005).
[6] Chang-Kuo Liang, Qubit-qubit Entanglement and Its Analysis, M. Sc. thesis, Dept.
of Physics, National Cheng Kung University (2010).
[7] J. J. Sakurai, Modern Quantum Mechanics(Revised Edition), by Addison-Wesley
Publishing Company, p.4-6, p.210-217, (1994).
[8] W. R. Hamilton, On quaternions, or on a new system of imaginaries in algebra,
Philosophical Magazine, Vol. 25, n 3, p.489-495. (1844).
[9] W. R. Hamilton, Elements of quaternions, Edited by W. E. Hamilton, University
of Dublin Press(1866).
[10] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, Pro-
posed Experiment to Test Local Hidden-Variable Theories, Phys. Rev. Lett. 23,
880-884 (1969).
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