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系統識別號 U0026-2908201914224500
論文名稱(中文) 量子糾纏態潛在的傳態能力
論文名稱(英文) Hidden Teleportation Power For Entangled Quantum State
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) 李峻禕
研究生(英文) Jyun-Yi Li
學號 l26064268
學位類別 碩士
語文別 英文
論文頁數 34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 量子傳態  局域性篩選器  保真度  單態比 
英文關鍵字 teleportation  local filtering  fidelity  singlet fraction 
學科別分類
中文摘要 透過共享一對最大糾纏態,理想的量子傳態可以將一未知的d維量子態從一處完整的遙傳至另一處,若Alice和Bob只共享了古典資源,則傳態的保真度,即,Alice欲傳的態和Bob拿到的態兩者的最大平均保真度為fc=2/(d+1),這個值對應到了單態比Fc=1/d。如果Alice和Bob共享了一對傳態保真度ffc(F>Fc),則我們說量子糾纏態ρ具有潛在的傳態能力。在這份研究工作內,我們探究:(1)有一個參數、兩個d維量子位元族的量子糾纏態以及Werner state的潛在傳態能力,(2)局域性篩選器成功的機率以及有多少傳態保真度可以藉由局域性篩選器來增加,兩者之間的關係,(3)將我們得到的結果和Rains的半定程式做比較,其考慮所有跡數保持的正局部轉置操作來最大化傳態保真度,(4)直接最大化單態比和最大化整體傳態保真度之間的差異,(5)給予一個如何用Mach-Zehnder干涉儀來測量兩個未知量子態的光子的例子。
英文摘要 An ideal quantum teleportation transfers an unknown d-dimensional quantum state intact from one party to another via the use of a maximally entangled state. If Alice and Bob only share a classical resource, the teleportation fidelity, i.e., the maximal average fidelity between the state to be teleported and the state received is at most fc=2/(d+1), which corresponds to singlet fraction Fc=1/d. If they share an entangled state ρ with teleportation fidelity fFc), we say that ρ has hidden teleportation power. Here, we investigate (1) the hidden teleportation power of a one-parameter family of entangled states and Werner state, (2) the trade-off between the success probability of local filtering and the extent to which the teleportation fidelity can be increased by this means,(3) the upper bound obtained by Rains’s semidefinite program [13], (4) difference between maximizing the singlet fraction after local filtering and maximizing cost function, (5) we also give an example of Mach-Zehnder interferometer to show how to measure the fidelity [5] of two photons in unknown states.
論文目次 摘要 i
Abstract ii
Acknowledgements iii
Table of Contents iv
List of Tables v
List of Figures vi
Nomenclature viii
Chapter 1. Introduction 1
1.1 Standard quantum teleportation 1
1.2 d-dimensional quantum teleportation 2
1.3 Teleportation power 3
1.4 Local filtering operations and hidden teleportation power 4
1.5 Our work 5
Chapter 2. Hidden Teleportation Power 6
2.1 Hidden teleportation power for two-qubit quantum state 6
2.2 Hidden teleportation power for higher-dimensional quantum state 9
2.3 Numerical Results 11
2.4 Rains’s semidefinite program 12
2.5 PPT symmetric extension 18
2.6 Maximizing singlet fraction vs maximizing cost function 19
2.7 One and two local filters 19
Chapter 3. Hidden teleportation power for Werner state 24
3.1 Numerical result 24
3.2 Conjecture 25
Chapter 4. Fidelity measure for two unknown quantum states 28
4.1 How to measure the fidelity of two unknown quantum state? 28
4.2 Mach-Zehnder interferometer 28
Chapter 5. Conclusion 32
References 34
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[13] E. M. Rains. A semidefinite program for distillable entanglement. IEEE Transactions on Information Theory, 47(7):2921–2933, Nov 2001.
[14] G. N. M. Tabia. private communication, 2019.
[15] Frank Verstraete and Henri Verschelde. Optimal teleportation with a mixed state of two qubits. Phys. Rev. Lett., 90:097901, Mar 2003.
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