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研究生: 劉沛樺
Liu, Pei-Hua
論文名稱: Topics on quantum entanglement: anti-Unruh phenomena and holographic quantum energy teleportation
Topics on quantum entanglement: anti-Unruh phenomena and holographic quantum energy teleportation
指導教授: 林豐利
Lin, Feng-Li
學位類別: 博士
Doctor
系所名稱: 物理學系
Department of Physics
論文出版年: 2017
畢業學年度: 105
語文別: 英文
論文頁數: 141
中文關鍵詞: EntanglementDecoherenceQuantum energy teleportationTopological qubitHolographicAdS/CFT
英文關鍵詞: Entanglement, Decoherence, Quantum energy teleportation, Topological qubit, Holographic, AdS/CFT
DOI URL: https://doi.org/10.6345/NTNU202201892
論文種類: 學術論文
相關次數: 點閱:125下載:28
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  • 無中文摘要

    Two topics on entanglement are concerned in this thesis: One is the decoherence patterns of a topological qubit made of two Majorana zero modes in the generic linear and circular motions and the other is a simplified protocol of quantum energy teleportation (QET) for the holographic conformal field theory in three-dimensional anti-de Sitter space with or without a black hole.
    On the first topic, the exact reduced dynamics without Markov approximation is shown. For general time scale, the acceleration causes thermalization as expected by Unruh effect. However, for the short-time scale, the rate
    of decoherence is anti-correlated with the acceleration, as a kind of decoherence impedance. This is in fact related to the “anti-Unruh" phenomenon previously found by studying the transition probability of Unruh-DeWitt detector. Besides, the information backflow is observed by some time modulations of coupling constant or acceleration. Moreover, it also shows that some incoherent accelerations of the constituent Majorana zero modes can preserve the coherence instead of thermalizing it.
    On the second topic, as a tentative proposal, the standard QET is simplified by replacing Alice’s local measurement with the local projection. At the same time, Bob’s local operation of the usual QET for extracting energy is mimicked by deforming the UV surface with a local bump. Adopting the
    surface-state duality, this deformation corresponds to local unitary. In this protocol, the extraction energy is always positive. Moreover, the ratio of extraction energy to the injection one is an universal function of the UV surface deformation profile.

    Contents Acknowledgements ii Abstract iii 1 Introduction 1 1.1 Quantum decoherence 3 1.1.1 Environment-induced decoherence 3 1.1.2 Feynman-Vernon and Schwinger-Keldysh 6 1.1.3 Quantum Brownian motion and Langevin equation 10 1.2 Unruh effect and toplogical qubit 14 1.2.1 Unruh effect and UDW model 15 1.2.2 Generic world line 18 1.2.3 Topological qubit 21 1.3 AdS/MERA correspondence 25 1.3.1 AdS/CFT correspondence 26 1.3.2 RT formula 28 1.3.3 MERA 33 1.3.4 AdS/MERA correspondence 37 1.3.5 cMERA and Surface/State correspondence 39 2 Decoherence of Topological Qubits 45 2.1 Introduction 46 2.2 Dynamics of open system for Majorana modes 46 2.2.1 Open system for Majorana modes 47 2.2.2 Reduced density matrix for Majorana probe 48 2.3 Decoherence patterns of topological qubits 52 2.3.1 Single topological qubit 54 2.3.2 Two topological qubits 55 2.3.3 Summary of decoherence patterns 57 3 Decoherence of Topological Qubit in Linear and Circular Motions: Decoherence Impedance, Anti-Unruh and Information Backflow 59 3.1 Introduction 60 3.2 Topological Qubits and their reduced dynamics 64 3.3 Formalism for the reduced dynamics of a moving topological qubit 66 3.3.1 Formalism 67 3.3.2 Environmental spectral densities and “influence functional" 70 3.3.3 Transition probability from reduced dynamics 73 3.4 Reduced dynamics of topological qubit in linear motions 76 3.4.1 “Overtaking" phenomenon: Constant acceleration 76 3.4.2 “Overtaking" phenomenon: Constant velocity 79 3.4.3 Decoherence Impedance and “Anti-Unruh" 81 3.4.4 Information backflow and time modulation 84 3.4.5 Frame dependence for incoherent motions due to non- locality 88 3.5 Reduced dynamics of topological qubit in circular motion 90 3.5.1 “Overtaking" phenomenon without frame issue: Con- stant angular velocity 91 3.5.2 Decoherence Impedance and “Anti-Unruh" 93 3.5.3 Modulation of switching function 93 3.5.4 Modulation of angular velocity 95 Appendix 97 3.A Evaluation of influence functional by the merging formula of OPE 97 3.B Spectral density and real-time correlators 98 3.C Transition probability 99 3.D Causal condition in the comoving coordinates 100 3.D.1 Linear acceleration: position difference 100 3.D.2 Linear acceleration: acceleration difference 100 3.D.3 Circular motion of constant angular velocity 100 4 Towards Holographic Quantum Energy Teleportation 102 4.1 Introduction 102 4.2 Toy QET model 104 4.2.1 A qubit model for QET 104 4.2.2 Schematic holographic QET protocol 107 4.3 Towards holographic QET 111 4.3.1 Holographic local projection operation 111 4.3.2 Holographic local unitary operation 115 4.4 Holographic QET at finite temperature 118 4.4.1 Finite temperature LPO from a conformal map 119 4.4.2 Energy extraction at finite temperature 121 Appendix 122 4.A Energy density profile for infinitesimal holographic local operations 122 5 Conclusion 124 Bibliography 129

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