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系統識別號 U0026-2908201917141200
論文名稱(中文) 無共享座標系的多體非局域性
論文名稱(英文) Multipartite Bell-inequality violation using randomly chosen triads
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 107
學期 2
出版年 108
研究生(中文) 楊士賢
研究生(英文) Shih-Xian Yang
電子信箱 ubiquitous89@gmail.com
學號 l26061016
學位類別 碩士
語文別 英文
論文頁數 30頁
口試委員 指導教授-梁永成
口試委員-徐立義
口試委員-傑洛
口試委員-Jeba
中文關鍵字 貝爾不等式  多體相關性  隨機量測 
英文關鍵字 Bell Inequality  Multipartite Correlation  Random Measurements 
學科別分類
中文摘要 我們研究多體的糾纏態 (Greenberger-Horne-Zeilinger state, GHZ) 在隨機選取量測的情況下違反貝爾不等式 (Bell inequality) 的機率。受之前研究二體的相關工作啟發,我們關注如下的貝爾情境 (Bell scenario):在情境中的每一個參與者 (party) 會從三個互不偏差的量測基底 (mutually unbiased bases) 中選擇兩個作為他們的量測。而每個參與者的三個基底都是隨機且均勻的選。在這樣的情況下探討能不能夠違反貝爾不等式。我們的數值計算結果顯示在四體以上的情況,我們都可以找到一組量測(每個參與者三選二為一組)違反貝爾不等式(除了零測度集外,a set of measure zero)。
並且對白噪音 (white noise) 的忍受度高,這暗示了原則上在一個貝爾實驗中,可以不用建立共享座標系也能有非局域的特性。
英文摘要 We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen bases on a multipartite Greenberger-Horne-Zeilinger
state. Inspired by previous work in the bipartite scenario, we consider specifically the case where each party performs measurements on bases that form a triad on the Bloch sphere.
As with the bipartite scenario, our numerical results for the tripartite, 4-partite, 5-partite and 6-partite scenario suggest that if each triad is randomly, but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure zero) finds correlations that violate a Bell inequality. In addition, these quantum violations of a Bell inequality appear to be fairly resistant to white noise, indicating that such a demonstration can in principle be performed in an experimental situation without sharing a global reference frame.
論文目次 Table of Contents
摘要 i
Abstract ii
Acknowledgments iii
Table of Contents iv
List of Tables v
List of Figures vi
Nomenclature vii

Chapter 1 Introduction 1
1.1 The Need of Shared Reference Frame . . . . . 2

Chapter 2 Preliminary 6
2.1 Probability of Violation . . . . . . . . . . 6
2.2 Concept of Probability Space . . . . . . . . 8
2.3 k-producibility . . .. . . . . . . . . . . . 9

Chapter 3 Probability of Violation of
Bell Inequalities 10
3.1 Results of Probability of Violation from
Mermin inequality . . . . . . . . . . . . . . 13
3.2 Results of Probability of Violation from
Bell inequality in Tripartite Scenario . . . . 17
3.3 Results of Probability of Violation from
7 th Sliwa and FG . . . . . . . . . . 17

Chapter 4 Robustness of the Scenario 20
4.1 Visibility . . . . . . . . . . . . . . . . 20
4.2 Results of Visibility from Linear
Programming . . . . . . . . . . . . . . . . . 20

Chapter 5 Related Work 23

Chapter 6 Conclusion 27
References 28
Appendix A Mermin inequalities 30
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