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研究生: 潘鳳鳴
Pan Feng-Ming
論文名稱: 量子纠缠在相對論性時空下的影響
Entanglement and Relativity
指導教授: 林豐利
Lin, Feng-Li
學位類別: 碩士
Master
系所名稱: 物理學系
Department of Physics
論文出版年: 2011
畢業學年度: 99
語文別: 英文
論文頁數: 40
中文關鍵詞: 量子纠缠相對論性時空
英文關鍵詞: Entanglement, Relativity, von Neumann entropy, Concurrence, Negativity
論文種類: 學術論文
相關次數: 點閱:263下載:0
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  • 我們介紹了量子纠缠在相對論性時空下的影響。第二章介紹了量子纠缠(純態、混和態、量子纠缠的判定、量子纠缠的度量)。第三章介紹了勞侖茲變換在量子力學下的表示 - Wigner旋轉。第四章討論了三個量子纠缠的度量(von Neumann entropy, Concurrence, Negativity)分別在 Minkowski 空間以及彎曲空間下之影響。

    We study the entanglement in the relativistic framework. The bipartite quantum state can be classi ed into pure state or mixed state. One can judge if the pure state is entangled or not by Schmidt decomposition, and the bi-partite entanglement of pure state is quanti ed by the von Neumann entropy. On the other hand, we adopt the positive partial transpose (PPT) criterion to study the entanglement for
    the mixed separable states, and quantify it by evaluating the quantities such as the concurrence and negativity. We study the properties of von Neumann entropy, concurrence and negativity under Lorentz transformation. Some examples for the entanglement in the weak and strong gravitational elds are discussed.

    1. Introduction 3 2. Bipartite Entanglement 6 2.1 Density matrix and Reduced density matrices 6 2.2 Pure state 8 2.2.1 De nition 8 2.2.2 Schmidt decomposition 9 2.2.3 von Neumann entropy 10 2.3 Mixed state 11 2.3.1 De nition 11 2.3.2 PPT criterion 12 2.3.3 Lower bound for Mixed states 14 2.3.4 Concurrence 16 2.3.5 Negativity 17 3. Wigner rotation of massive Spin-1/2 particle 19 3.1 One particle state 19 3.1.1 Standard boost 20 3.2 Minkowski space 21 3.3 Gravitational eld 22 3.3.1 Local inertial frame 23 3.3.2 Spin precession 24 3.4 Spin entropy is not Lorentz invariant 25 4. Entanglement under Wigner rotation 27 4.1 Entanglement in the Minkowski space 28 4.1.1 von Neumann entropy in the Minkowski space 28 4.1.2 Concurrence in the Minkowski space 29 4.1.3 Negativity in the Minkowski space 30 4.2 Entanglement in gravitational field 31 4.2.1 Fall to a Black hole and circular geodesics 32 4.2.2 von Neumann entropy in gravitational field 36 4.2.3 Concurrence in gravitational field 36 4.2.4 Negativity in gravitational field 37 5. Conclusion 38

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