八維超糾纏非局域性的實驗設計

Abstract

量子力學對於現今的科學佔有重要的地位，但是它的量子非局性一直是很多物理學家質疑的地方，而愛因斯坦則認為量子力學是不完備的因此在西元1935年提出EPR悖論，到了西元1965年貝爾提出了貝爾不等式做為驗證量子力學完備性的數學工具，物理學家為了驗證高維糾纏的量子非局域性在西元2001年又將貝爾不等式推廣成高維貝爾不等式。而本論文則是探討如何利用光子的偏振、時間-能量與軌道角動量三種自由度去設計一個可以驗證八維超糾纏非局域性的實驗設計。而這樣的實驗設計還可將它應用於量子密鑰傳輸，並且可以利用八維超糾纏量子非局域的特性提升量子密鑰傳輸的安全性及傳輸效率。 本論文第一章首先介紹使用超糾纏的優點和基本原理，第二章介紹超糾纏的理論以及驗證糾纏態的量子非局域性會使用到的數學工具，第三章介紹超糾纏實驗的歷史發展，第四章一開始介紹一些實驗設計會使用到的元件和基本原理，接下來介紹如何利用光子的偏振、時間-能量與軌道角動量設計出各種四維的高維貝爾不等式實驗設計，之後再將這三種自由度全部糾纏在一起形成八維超糾纏非局域性的實驗設計，最後介紹如何利用高維貝爾不等式去研究本論文實驗設計的量子非局域性及其意義，並探討如何將它應用於量子密鑰傳輸並分析它的安全性以及傳輸效率，第五章對研究做出結論並說明未來可以做的研究及其應用。

Quantum mechanics plays an important role in the present science.But its quantum non-locality has been questioned by many physicists.And Einstein argues that quantum mechanics is incomplete and therefore proposes EPR paradox in AD 1935.In 1965, Bell proposed the Bell's inequality as a mathematical tool to verify the completeness of quantum mechanics.In order to verify the quantum nonlocality of the high-dimensional entanglement, the physicist, in 2001, extended the Bell inequality into high-dimensional Bell's inequality.In this paper, we discuss how to use the three degrees of freedom of photon polarization, time-energy and orbital angular momentum to design an experimental design that can verify the non-localized eight-dimensional hyper-entanglement.And such experimental design can also be applied to quantum key transmission.And can use the eight-dimensional entangled quantum non-local characteristics to enhance the security and transmission efficiency of quantum key transmission. The first chapter of this paper first introduces the advantages and the basic principle of using hyper-entanglement.Chapter 2 introduces the theory of hyper-entanglement and the mathematical tools used to verify the quantum nonlocality of the entangled state.The third chapter introduces the historical development of hyper-entanglement experiments.The fourth chapter begins by introducing some of the components and fundamentals that the experimental design will use.Then, introduce how to use the photon polarization, time - energy and orbital angular momentum to design a variety of four - dimensional Bell inequality experimental designs.And then these three degrees of freedom all together to form eight-dimensional hyper-entanglement non-local experimental design.Finally, introduce how to use the high-dimensional Bell inequality to study the quantum nonlocality of experimental design and its significance.And explore how it can be applied to quantum key transmission and analyze its security and transmission efficiency.Chapter 5 concludes the study and explains what can be done in the future and its application.