跳到主要內容

臺灣博碩士論文加值系統

(44.220.44.148) 您好!臺灣時間:2024/06/21 15:49
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

: 
twitterline
研究生:吳青龍
研究生(外文):Ching-Long Wu
論文名稱:維格納轉換和糾纏態的分析
論文名稱(外文):Wigner transforms and analysis of entanglement
指導教授:許祖斌
指導教授(外文):Chopin Soo
學位類別:碩士
校院名稱:國立成功大學
系所名稱:物理學系碩博士班
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:59
中文關鍵詞:糾纏
外文關鍵詞:Wigner transformentanglement
相關次數:
  • 被引用被引用:0
  • 點閱點閱:192
  • 評分評分:
  • 下載下載:16
  • 收藏至我的研究室書目清單書目收藏:0
  本篇論文中介紹和位置、動量、自旋有關的維格納方程,然後我們主要考慮自旋部分的維格納方程,利用它來分析雙自旋的糾纏現象。我們也得到一個對密度矩陣分離性﹝”古典相關”或是”無糾纏”﹞的廣義必要條件。這個方法可以推廣到兩個自旋為n的狀況,而且也符合量子場論的要求和勞侖茲不變性。
 We study the Wigner function which is dependent on position, momentum, and spin; and apply the matrix of its spin part W, to the analysis of bipartite spin entanglement. We also derived a general necessary condition for separability (”classical correlation” or “non-entanglement”) of the density matrix. The method can be generalized to bipartite spin-n (or generic N = 2n + 1-state subsystems) and made compatible with the requirements of quantum field theory and Lorentz symmetry.
1 Introduction ......................................................1
1.1 Density matrix of mixed states of Bose and Fermi statistics .....1
1.2 Wigner Transform for spin-0 states ..............................2
1.3 Special case of two identical spin-0 particles ..................5
2.Wigner Transform for spin-1/2 system ..............................8
2.1 Introduction toWigner function for spin-1/2 states; and the
Clauser-Horne-Shimony-Holt (CHSH) relation ..........................8
2.1.1 The density matrix ............................................8
2.1.2 Wigner transforms and Quantum Field Theory (QFT) ..............9
2.1.3 Introduction to Wigner function for spin- 1/2 states ..........9
2.1.4 Introduction to (CHSH) .......................................11
2.2 Tr(WW^T) .......................................................12
2.2.1 General density matrix .......................................12
2.2.2 Density matrix of classically correlated system ..............13
2.2.3 Density matrix of pure states ................................13
2.2.4 Werner density matrix ........................................15
2.3 Tr(WW^TWW^T ) ..................................................16
2.3.1 General density matrix .......................................16
2.3.2 Density matrix of classically correlated system ..............17
2.3.3 Density matrix of pure states ................................18
2.3.4 Werner density matrix ........................................20
2.4 Tr(WW^TWW^TWW^T ) ..............................................21
2.4.1 General density matrix .......................................21
2.4.2 Density matrix of classically correlated system ..............27
2.4.3 Density matrix of pure states ................................30
2.4.4 Werner density matrix ........................................34
2.5 Eigenvalues of WW^T ............................................37
2.5.1 Cubic equation ...............................................38
2.5.2 Eigenvalues of WW^T for pure state system ....................38
2.5.3 Eigenvalues for classically correlated system ................40
2.5.4 Eigenvalues for Werner density matrix ........................40
2.6 Wigner transform and positivity of partial transpose (PPT) of
the density matrix .................................................42
2.6.1 Introduction to PPT ..........................................42
2.6.2 Wigner transforms and PPT ....................................42
2.6.3 PPT for Werner density matrix ................................43
2.6.4 Necessary condtion for classically correlated system in terns
of W ...............................................................43
2.6.5 Comparing Σ|λi|<=1 to PPT for Werner density matrix ........44
2.6.6 Explicit separability(decomposition) of Werner density matrix
(r <=1/3) ..........................................................45
3 Generalizing Wigner Transform to spin-n states ...................46
4 Conclusions ......................................................48
References .......................................................49
[1] E. P. Wigner, Physical Review, 40 (1932) 749-759; for a review, see also M. Hillery, R. F. O’Connell, M. O. Scully, and E. P. Wigner, Distribution Functions in Physics:Fundamentals, Physics Reports 106(3) (1984) 121.
[2] C. Sean Bohun, Reinhard Illner, Paul F. Zweifel, and Le Matematiche Vol. XlVI (1991) Fasc.I, 429-438.
[3] R. F. O’Connell and E. P. Wigner, Physical Review A, 30 (1984), 2613-2618.
[4] B. S. Tsirelson. Lett. Math. Phys.(1980),4:93
[5] M.Horodecki, R. Horodecki, and R. Horodecki, Phy. Lett. A 223,1 (1996).
[6] T. D. Newton, E. P. Wigner, Rev. Mod. Phys. 21, 400 (1949).
[7] A. Sanpera, R.Tarrach, and G. Vidal, e-print quant-ph/9707041
[8] C. Soo and C. Y. Lin, International Journal of Quantum Information 2 (2004) 183-200
[9] Murray R. Spiegel, John Liu, Mathematical Handbook of Formulas and Tables Second Edition.
[10] C. Y. Lin, C. Soo and C. L. Wu,Wigner transforms and criteria for separability, in preparation (2005).
[11] R. F. Werner, Phys. Rev. A. 40, 4277 (1989)
連結至畢業學校之論文網頁點我開啟連結
註: 此連結為研究生畢業學校所提供,不一定有電子全文可供下載,若連結有誤,請點選上方之〝勘誤回報〞功能,我們會盡快修正,謝謝!
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關論文