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研究生:李哲旭
研究生(外文):Che-ShuLee
論文名稱:純態雙分系統糾纏的精細描述
論文名稱(外文):Finer Characterizations ofPure Bipartite Entanglement
指導教授:許祖斌
指導教授(外文):Cho-Pin 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:2012
畢業學年度:100
語文別:英文
論文頁數:38
中文關鍵詞:糾纏純態雙分系統量化
外文關鍵詞:EntanglementPureBipartitePPTmeasure
相關次數:
  • 被引用被引用:0
  • 點閱點閱:154
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  • 下載下載:4
  • 收藏至我的研究室書目清單書目收藏:0
本論文提出了一個新的、對系統可分性充分必要的評判準則,而這個準則適用於任意有限維的純態雙分系統。並且我們也討論了與之對應的、對糾纏更精細的量化和描述(而不僅僅是作為糾纏與否的判斷)。基於這個評判準則,我們證明了著名的Peres-Horodecki positivity-of-partial-transform評判準則對純態雙分系統的可分性也是充分必要的。最後我們推導出了糾纏的最大值,並且也詳盡地給出了相應的最大糾纏態。
A new criterion necessary and sufficient for the separability of pure bipartite systems for arbitrary finite dimensions is demonstrated; and the corresponding finer quantitative measures or characterizations of entanglement (beyond mere separability or nonseparability determination) are discussed. Based on this criterion, we proved that the well-known Peres-Horodecki positivity-of-partial-transform criterion is also necessary and sufficient for separability in the case of pure bipartite systems. The maximum value of entanglement, and the corresponding maximally-entangled states are also worked out in detail.
References
[1] A. Einstein, B. Podolsky, and N. Rosen, Can quantum-mechanical description of physical reality be considered complete?, Phys. Rev. 47 777 (1935).
[2] E. Schrodinger, Discussion of Probability Relations between Separated Systems, Proceedings of the Cambridge Philosophical Society 31, 555-563, (1935).
[3] J.S. Bell, On the Einstein-Podolsky-Rosen paradox, Physic 1, 195 (1964).
[4] Alain Aspect, Philippe Grangier, and G erard Roger, Experimental Tests of Realistic Local Theories via Bell's Theorem, Phys. Rev. Lett. 47, 460 (1981).
[5] John F. Clauser, Michael A. Horne, Abner Shimony, and Richard A. Holt, Proposed Experiment to Test Local Hidden-Variable Theories, Phys. Rev. Lett. 23, 880-884 (1969).
[6] Charles H. Bennett, Gilles Brassard, Claude Crpeau, Richard Jozsa, Asher Peres, and William K. Wootters, Teleporting an unknown quantum state via dual classical
and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 18951899 (1993).
[7] See for instance, Quantum Computation and Quantum Information, Michael A. Nielsen, Isaac L. Chuang. Cambridge University Press, New York, 2000
[8] C. H. Bennett, H. Bernstein, S. Popescu and B. Schumacher, Concentrating partial entanglement by local operations, Phys. Rev. A 53, 2046 (1996).
[9] Martin B. Plenio, S. Virmani, An introduction to entanglement measures, Quant.Inf. Comput.7:1-51 (2007).
[10] A. Peres, Separability Criterion for Density Matrices, Phys. Rev. Lett. 77, 1413 (1996).
[11] M. Horodecki, P. Horodecki and R. Horodecki, Separability of mixed states necessary and sufficient conditions, Phys. Lett. A223, 8 (1996).
[12] Chang-Kuo Liang, Qubit-qubit entanglement and its analysis, M. Sc. thesis, Dept. of Physics, National ChengKung University (2010).
[13] Kai-Siang Neo, A study of the Clauser-Horne-Shimony-Holt relation, M. Sc. thesis, Dept. of Physics, National Cheng Kung University (2005).
[14] P. Busch, and Pekka J. Lahti, Remarks on separability of compound quantum systems and time reversal, Found. Phys. Lett. 10, 113 (1997).
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