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研究生: 陳嘉國
Chen, Chia-Kuo
論文名稱: 量化量子隱形傳態及其應用
Quantifying Quantum Teleportation and Its applications
指導教授: 李哲明
Li, Che-Ming
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2019
畢業學年度: 107
語文別: 英文
論文頁數: 76
中文關鍵詞: 量子隱形傳態量子過程量子糾纏量子操控性
外文關鍵詞: quantum teleportation, quantum-mechanical process, entanglement, Einstein- Podolsky-Rosen steering
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  • 量子隱形傳態(Quantum teleportation) 利用了量子量測與最大糾纏的愛因斯坦-波多爾斯基-羅森粒子對,完成於相隔兩地之間未知量子態的傳輸,對量子計算與量子資訊至關重要。一般普遍認知上,所有的糾纏態都能夠去展現所謂的“非古典隱形傳態’,而這樣的非古典隱形傳態不能被“量測-準備策略”(measure-prepare strategy)所模擬;於此,我們證明了並非所有的非古典隱形傳態皆為純然的量子力學過程。更準確地說,存在著更強的古典過程模型,而量測-準備策略是它的一個可被描述的特例;超越這樣的古典過程模型所能描述的過程意味著“真正的量子隱形傳態”,而其粒子對的狀態與量測皆具純然量子力學特性。我們證明了是量子操控性而非量子糾纏驅動了真正的量子隱形傳態。量子糾纏運用於量子隱形傳態上;而真正的多體糾纏可運用於多人參與的量子隱形傳態上,對此,我們從過程的角度,量化一個過程產生純的多體糾纏的能力。對於量子資訊處理,如遠端準備量子態協定(remote state preparation) 或是複合量子系統的量子隱形傳態,愛因斯坦-波多爾斯基-羅森粒子對也同樣是不可或缺;對這樣的量子資訊處理,我們的結果亦為實現可信賴的量子資訊任務提供了客觀與嚴謹的指標。

    Quantum teleportation is a method for utilizing quantum measurements and the maximally entangled Einstein-Podolsky-Rosen (EPR) pair to transmit an unknown quantum state, which provides the power crucial for quantum computation and uantum information. It is well known that all entangled states demonstrate so-called “nonclassical teleportation” that cannot be simulated by the seminal classical measure-prepare strategy. Herein, we reveal that not all nonclassical teleportations are truly quantum-mechanical. Rather, there exists a stronger classical-teleportation model, which includes the measure-prepare procedure for teleportation as a special case, that can describe certain nonclassical teleportations. Invalidating such a classical model implies genuine quantum teleportation wherein both the pair state and the measurement are truly quantum-mechanical. We show that PR steering empowers genuine quantum teleportations, rather than entanglement. Our results show a compelling benchmark for implementing quantum-information processing where EPR pairs are indispensable, such as remote state preparation and general teleportation for composite quantum systems.

    摘要 i Abstract ii 致謝 iii Table of Contents iv List of Figures vii Nomenclature viii Chapter 1. Introduction 1 1.1. Background . . . . . . . . . . . . . . . . . . . . . . . .1 1.2. Motivation . . . . . . . . . . . . . . . . . . . . . . . 2 1.3. Purpose . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4. Outline . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2. Essential Knowledge and Tools 6 2.1. Postulates of quantum mechanics . . . . . . . . . . . . . 6 2.1.1. Postulate 1 – State space . . . . . . . . . . . . . . . 6 2.1.2. Postulate 2 – Quantum evolution . . . . . . . . . . . . 8 2.1.3. Postulate 3 – Quantum measurement . . . . . . . . . . . 9 2.1.4. Postulate 4 – Composite system . . . . . . . . . . . . 11 2.2. The density operator . . . . . . . . . . . . . . . . . . 13 2.3. Quantum tomography . . . . . . . . . . . . . . . . . . . 16 2.3.1. Quantum state tomography . . . . . . . . . . . . . . . 16 2.3.2. Quantum process tomography . . . . . . . . . . . . . . 17 2.4. Einstein-Podolsky-Rosen Steering . . . . . . . . . . . . 20 2.5. Quantum teleportation . . . . . . . . . . . . . . . . . 21 Chapter 3. Quantifying Genuine Quantum Teleportation 24 3.1. Basic concept . . . . . . . . . . . . . . . . . . . . . 24 3.1.1. Characterizing teleportation processes . . . . . . . . 26 3.1.2. Implication of the measure-prepare strategy . . . . . 28 3.1.3. General model of classical teleportation . . . . . . . 29 3.1.4. Genuine quantum teleportaion . . . . . . . . . . . . . 30 3.2. Approaches for quantitatively characterizing teleportation 31 3.2.1. Fidelity criteria . . . . . . . . . . . . . . . . . . . 31 3.2.2. Quantum composition . . . . . . . . . . . . . . . . . . 33 3.2.3. Process robustness . . . . . . . . . . . . . . . . . . 33 3.3. Examples . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.1. Measure-prepare strategy . . . . . . . . . . . . . . . . 35 3.3.2. Noisy teleportation . . . . . . . . . . . . . . . . . . 36 3.4. Resources required for genuine quantum teleportation . . . 39 3.5. Discussion and Applications . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5.1. Teleportation for composite quantum systems . . . . . . 40 3.5.2. Simulating any dynamical process with Chi_CT . . . . . . . 42 3.5.3. Identifying processes of quantum information . . . . . . 42 Chapter 4. Quantifying Genuine Multipartite Entanglement Generation 45 4.1. Genuine Multipartite Entanglement and biseparable states . 45 4.1.1. Positive partial transpose criterion . . . . . . . . . . 45 4.1.2. Entanglement witness . . . . . . . . . . . . . . . . . 46 4.2. Genuine multipartite entanglement generating process and incapable process 47 4.3. Approaches for quantifying genuine multipartite entanglement generation 48 4.3.1. Genuine multipartite entanglement generating robustness 48 4.3.2. Genuine multipartite entanglement generating fidelity criteria 49 4.4. Quantifying genuine multipartite entanglement generation . 50 4.4.1. Quantifying 2-qubit genuine multipartite entanglement generation 50 4.4.2. Quantifying 3-qubit genuine multipartite entanglement generation 55 4.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . 60 Chapter 5. Summary and outlook 61 5.1. Summary . . . . . . . . . . . . . . . . . .. . . . . . . 61 5.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . 62 References 64 Appendix A. The paper submitted for publication 68

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