Quantum Information Processing by Gerd Leuchs and Thomas Beth


165a74fec32ab0a-261x361.jpg Author Gerd Leuchs and Thomas Beth
Isbn 9783527405411
File size 41.26MB
Year 2005
Pages 471
Language English
File format PDF
Category physics


 

T. Beth, G. Leuchs (Eds.) Quantum Information Processing 2., revised and enlarged Edition Quantum Information Processing Second, revised and enlarged Edition Edited by Thomas Beth, Gerd Leuchs WILEY-VCH Verlag GmbH & Co. KGaA Editors Prof. Dr.-Ing. Thomas Beth Universität Karlsruhe Fakultät für Informatik [email protected] Prof. Dr. Gerd Leuchs Universität Erlangen Institut für Optik, Information und Photonik [email protected] 1st Edition 2003 2nd Edition 2005 All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: Applied for British Library Cataloging-in-Publication Data: A catalogue record for this book is available from the British Library Bibliographic information published by Die Deutsche Bibliothek Cover Picture Main: Poincaré sphere showing quantum polarisation states Courtesy of Christine Silberhorn and Joel Heersink Lower right: Diagram for a controlled NOT-gate Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at . © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Printed in the Federal Republic of Germany Printed on acid-free paper Printing Strauss GmbH, Mörlenbach Bookbinding Litges & Dopf Buchbinderei GmbH, Heppenheim ISBN-13: 978-3-527-40541-1 ISBN-10: 3-527-40541-0 Contents IX 13 Quantum Dynamics of Vortices and Vortex Qubits (A. Wallraff, A. Kemp, and A. V. Ustinov) 13.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 13.2 Macroscopic Quantum Effects with Single Vortices . . . . 13.2.1 Quantum Tunneling . . . . . . . . . . . . . . . . 13.2.2 Energy Level Quantization . . . . . . . . . . . . . 13.3 Vortex–Antivortex Pairs . . . . . . . . . . . . . . . . . . . 13.3.1 Thermal and Quantum Dissociation . . . . . . . . 13.3.2 Energy Levels of a Bound Vortex–Antivortex Pair . 13.4 The Josephson Vortex Qubit . . . . . . . . . . . . . . . . 13.4.1 Principle of the Vortex Qubit . . . . . . . . . . . . 13.4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . 13.4.3 Perturbative Calculation of Vortex Potential . . . . 13.4.4 Quantum Mechanics of a Vortex in a Double Well . 13.4.5 Depinning Current and Qubit Readout . . . . . . . 13.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 162 163 163 165 167 167 171 173 174 175 177 179 180 182 183 14 Decoherence in Resonantly Driven Bistable Systems (S. Kohler and P. Hänggi) 14.1 Introduction . . . . . . . . . . . . . . . . . . . . 14.2 The Model and its Symmetries . . . . . . . . . . 14.3 Coherent Tunneling . . . . . . . . . . . . . . . . 14.4 Dissipative Tunneling . . . . . . . . . . . . . . . 14.5 Conclusions . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 186 186 188 192 196 197 15 Entanglement and Decoherence in Cavity QED with a Trapped Ion (W. Vogel and Ch. DiFidio) 15.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15.2 Decoherence Effects . . . . . . . . . . . . . . . . . . . . . . . . 15.3 Greenberger–Horne–Zeilinger State . . . . . . . . . . . . . . . . 15.4 Photon-number Control . . . . . . . . . . . . . . . . . . . . . . . 15.5 Entanglement of Separated Atoms . . . . . . . . . . . . . . . . . 15.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 198 199 201 203 205 207 207 16 Quantum Information Processing with Ions Deterministically Coupled to an Optical Cavity (M. Keller, B. Lange, K. Hayasaka, W. Lange, and H. Walther) 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.2 Deterministic Coupling of Ions and Cavity Field . . . . . . . . . . . . . . . 16.3 Single-ion Mapping of Cavity-Modes . . . . . . . . . . . . . . . . . . . . 16.4 Atom–Photon Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.5 Single-Photon Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209 209 210 212 215 217 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents Preface XV List of Contributors 1 XIX Algorithms for Quantum Systems — Quantum Algorithms (Th. Beth, M. Grassl, D. Janzing, M. Rötteler, P. Wocjan, and R. Zeier) 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Fast Quantum Signal Transforms . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Quantum Error-correcting Codes . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Efficient Decomposition of Quantum Operations into Given One-parameter Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.5 Simulation of Hamiltonians . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 1 3 5 8 10 2 Quantum Information Processing and Error Correction with Jump Codes (G. Alber, M. Mussinger, and A. Delgado) 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Invertible Quantum Operations and Error Correction . . . . . . . . . . . 2.3 Quantum Error Correction by Jump Codes . . . . . . . . . . . . . . . . . 2.3.1 Spontaneous Decay and Quantum Trajectories . . . . . . . . . . 2.3.2 Jump Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Universal Quantum Gates in Code Spaces . . . . . . . . . . . . . . . . . 2.4.1 Universal Sets of Quantum Gates for Qudit-Systems . . . . . . . 2.4.2 Universal One-Qutrit Gates . . . . . . . . . . . . . . . . . . . . 2.4.3 A Universal Entanglement Gate . . . . . . . . . . . . . . . . . . 2.5 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 14 15 17 17 19 21 21 22 23 25 26 3 Computational Model for the One-Way Quantum Computer: Concepts and Summary (R. Raussendorf and H. J. Briegel) 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The QCC as a Universal Simulator of Quantum Logic Networks 3.3 Non-Network Character of the QCC . . . . . . . . . . . . . . . 3.4 Computational Model . . . . . . . . . . . . . . . . . . . . . . . 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 28 30 35 36 42 42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VI 4 5 6 Contents Quantum Correlations as Basic Resource for Quantum Key Distribution (M. Curty, O. Gühne, M. Lewenstein, and N. Lütkenhaus) 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Background of Classical Information Theoretic Security . . . . . . . . 4.3 Link Between Classical and Quantum . . . . . . . . . . . . . . . . . . 4.4 Searching for Effective Entanglement . . . . . . . . . . . . . . . . . . 4.5 Verification Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.1 6-state Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 4-state Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 2-state Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Examples for Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Realistic Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increasing the Size of NMR Quantum Computers (S. J. Glaser, R. Marx, T. Reiss, T. Schulte-Herbrüggen, N. Khaneja, J. M. Myers, and A. F. Fahmy) 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Suitable Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Scaling Problem for Experiments Based on Pseudo-pure States . . . . . . . . 5.4 Approaching Pure States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Scalable NMR Quantum Computing Based on the Thermal Density Operator 5.6 Time-optimal Implementation of Quantum Gates . . . . . . . . . . . . . . . 5.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On Lossless Quantum Data Compression and Quantum Variable-length Codes (R. Ahlswede and N. Cai) 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Codes, Lengths, Kraft Inequality and von Neumann Entropy Bound . . . . . 6.2.1 The Codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Length Observable and Average Length of Codewords . . . . . . . . 6.2.3 Kraft Inequality and von Neumann Entropy Bound . . . . . . . . . . 6.2.4 Base Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Construct Long Codes from Variable-length Codes . . . . . . . . . . . . . . 6.4 Lossless Quantum Data Compression, if the Decoder is Informed about the Base Lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Code Analysis Based on the Base Length . . . . . . . . . . . . . . . . . . . 6.6 Lossless Quantum Data Compression with a Classical Helper . . . . . . . . . 6.7 Lossless Quantum Data Compression for Mixed State Sources . . . . . . . . 6.8 A Result on Tradeoff between Quantum and Classical Resources in Lossy Quantum Data Compression . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 44 45 46 49 51 51 51 52 53 54 55 55 58 58 59 62 62 63 64 67 68 70 70 71 71 72 72 73 73 74 75 76 79 80 81 Contents VII 7 Entanglement Properties of Composite Quantum Systems (K. Eckert, O. Gühne, F. Hulpke, P. Hyllus, J. Korbicz, J. Mompart, D. Bruß, M. Lewenstein, and A. Sanpera) 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Separability of Composite Quantum Systems . . . . . . . . . . . . . . 7.2.1 The Separability Problem . . . . . . . . . . . . . . . . . . . . 7.2.2 Results on The Separability Problem . . . . . . . . . . . . . . . 7.3 The Distillability Problem . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Results on the Distillability Problem . . . . . . . . . . . . . . . 7.4 Witness Operators for the Detection of Entanglement . . . . . . . . . . 7.4.1 Definition and Geometrical Interpretation of Witness Operators 7.4.2 Results on Witness Operators . . . . . . . . . . . . . . . . . . 7.5 Quantum Correlations in Systems of Fermionic and Bosonic States . . . 7.5.1 What is Different with Indistinguishable Particles? . . . . . . . 7.5.2 Results on Quantum Correlations for Indistinguishable Particles 7.5.3 Implementation of an Entangling Gate with Bosons . . . . . . . 7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 83 84 85 86 88 89 90 90 92 94 94 95 97 97 97 8 Non-Classical Gaussian States in Noisy Environments (S. Scheel and D.-G. Welsch) 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . 8.2 Gaussian States and Gaussian Operations . . . . . 8.2.1 Classicality . . . . . . . . . . . . . . . . . 8.2.2 CP Maps and Partial Measurements . . . . 8.2.3 Separability and Entanglement . . . . . . . 8.3 Entanglement Degradation . . . . . . . . . . . . . 8.4 Quantum Teleportation in Noisy Environments . . 8.4.1 Imperfect Teleportation . . . . . . . . . . . 8.4.2 Teleportation Fidelity . . . . . . . . . . . . 8.4.3 Choice of the Coherent Displacement . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 100 100 102 102 103 104 106 107 108 110 111 9 Quantum Estimation with Finite Resources (T. C. Bschorr, D. G. Fischer, H. Mack, W. P. Schleich, and M. Freyberger) 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Quantum Devices and Channels . . . . . . . . . . . . . . . . . . . 9.3 Estimating Quantum Channels . . . . . . . . . . . . . . . . . . . . 9.4 Entanglement and Estimation . . . . . . . . . . . . . . . . . . . . . 9.4.1 Estimation using Single Qubits . . . . . . . . . . . . . . . . 9.4.2 Estimation using Entangled States . . . . . . . . . . . . . . 9.5 Generalized Estimation Schemes . . . . . . . . . . . . . . . . . . . 9.5.1 Estimation with Two Channels . . . . . . . . . . . . . . . . 9.5.2 What is the Optimal Reference Channel? . . . . . . . . . . 9.5.3 Estimation with Werner States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 113 114 115 115 116 118 120 120 121 122 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VIII Contents 9.6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 10 Size Scaling of Decoherence Rates (C. S. Maierle and D. Suter) 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Decoherence Models . . . . . . . . . . . . . . . . . . . . . 10.3 Collective and Independent Decoherence . . . . . . . . . . . 10.4 Average Decoherence Rate as a Measure of Decoherence . . 10.5 Decoherence Rate Scaling due to Partially Correlated Fields 10.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 125 126 127 128 130 134 134 11 Reduced Collective Description of Spin-Ensembles (M. Michel, H. Schmidt, F. Tonner, and G. Mahler) 11.1 Introduction . . . . . . . . . . . . . . . . . . . . 11.2 Operator Representations . . . . . . . . . . . . . 11.3 Hamilton Models . . . . . . . . . . . . . . . . . 11.3.1 Symmetry-constrained Networks . . . . . 11.3.2 Topology-constrained Networks . . . . . 11.4 State Models . . . . . . . . . . . . . . . . . . . 11.4.1 Totally Permutation-symmetric Subspace 11.4.2 Collective 1-particle Excitations . . . . . 11.4.3 1-parameter Families of Non-pure States 11.4.4 Families of Separable States: “Modules” 11.5 Ensembles . . . . . . . . . . . . . . . . . . . . . 11.5.1 Trajectories and Ergodicity . . . . . . . . 11.5.2 Leakage and Storage Capacity . . . . . . 11.5.3 Mixing Strategies . . . . . . . . . . . . . 11.5.4 State Construction and Separability . . . 11.6 Summary and Outlook . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 135 135 138 138 139 140 140 140 141 141 141 142 144 146 147 147 148 12 Quantum Information Processing with Defects (F. Jelezko and J. Wrachtrup) 12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Properties of Nitrogen-vacancy Centers in Diamond . . . . . . . . . . . . . . 12.3 Readout of Spin State via Site-selective Excitation . . . . . . . . . . . . . . . 12.4 Magnetic Resonance on a Single Spin at Room Temperature . . . . . . . . . 12.5 Magnetic Resonance on a Single 13 C Nuclear Spin . . . . . . . . . . . . . . 12.6 Two-qubit Gate with Electron Spin and 13 C Nuclear Spin of Single NV Defect 12.7 Outlook: Towards Scalable NV Based Quantum Processor . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 150 150 152 155 156 158 160 160 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X Contents 16.6 Cavity-mediated Two-Ion Coupling . . . . . . . . . . . . . . . . . . . . . . 219 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 17 Strongly Coupled Atom–Cavity Systems (A. Kuhn, M. Hennrich, and G. Rempe) 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . 17.2 Atoms, Cavities and Light . . . . . . . . . . . . . 17.2.1 Field Quantization in a Fabry–Perot Cavity 17.2.2 Two-Level Atom . . . . . . . . . . . . . . 17.2.3 Three-Level Atom . . . . . . . . . . . . . 17.2.4 Adiabatic Passage . . . . . . . . . . . . . 17.3 Single-Photon Sources . . . . . . . . . . . . . . . 17.3.1 Vacuum-Stimulated Raman Scattering . . . 17.3.2 Deterministic Single-Photon Sequences . . 17.4 Summary and Outlook . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 223 223 223 224 225 227 228 229 230 233 233 18 A Relaxation-free Verification of the Quantum Zeno Paradox on an Individual Atom (Ch. Balzer, Th. Hannemann, D. Reiß, Ch. Wunderlich, W. Neuhauser, and P. E. Toschek) 18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.2 The Hardware and Basic Procedure . . . . . . . . . . . . . . . . . 18.3 First Scheme: Statistics of the Sequences of Equal Results . . . . . 18.4 Second Scheme: Driving the Ion by Fractionated π-Pulses . . . . . 18.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18.6 Survey of Related Work . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 237 238 241 243 246 247 249 19 Spin Resonance with Trapped Ions: Experiments and New Concepts (K. Abich, Ch. Balzer, T. Hannemann, F. Mintert, W. Neuhauser, D. Reiß, P. E. Toschek, and Ch. Wunderlich) 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Self-learning Estimation of Quantum States . . . . . . . . . . . . 19.3 Experimental Realization of Quantum Channels . . . . . . . . . . 19.4 New Concepts for QIP with Trapped Ions . . . . . . . . . . . . . 19.4.1 Spin Resonance with Trapped Ions . . . . . . . . . . . . . 19.4.2 Simultaneous Cooling of Axial Vibrational Modes . . . . 19.5 Raman Cooling of two Trapped Ions . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 251 252 254 256 257 260 261 263 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Controlled Single Neutral Atoms as Qubits (V. Gomer, W. Alt, S. Kuhr, D. Schrader, and D. Meschede) 265 20.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 20.2 Cavity QED for QIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Contents 20.3 Single Atom Controlled Manipulation . . . . . . . 20.4 How to Prepare Exactly 2 Atoms in a Dipole Trap? 20.5 Optical Dipole Trap . . . . . . . . . . . . . . . . . 20.6 Relaxation and Decoherence . . . . . . . . . . . . 20.7 Qubit Conveyor Belt . . . . . . . . . . . . . . . . 20.8 Outlook . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . XI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266 267 267 268 269 270 270 21 Towards Quantum Logic with Cold Atoms in a CO2 Laser Optical Lattice (G. Cennini, G. Ritt, C. Geckeler, R. Scheunemann, and M. Weitz) 21.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Entanglement and Beyond . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Quantum Logic and Far-detuned Optical Lattices . . . . . . . . . . . . . 21.4 Resolving and Addressing Cold Atoms in Single Lattice Sites . . . . . . 21.5 Recent Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 275 276 277 279 282 284 22 Quantum Information Processing with Atoms in Optical Micro-Structures (R. Dumke, M. Volk, T. Müther, F. B. J. Buchkremer, W. Ertmer, and G. Birkl) 22.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Microoptical Elements for Quantum Information Processing . . . . . . . 22.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.4 Scalable Qubit Registers Based on Arrays of Dipole Traps . . . . . . . . 22.5 Initialization, Manipulation and Readout . . . . . . . . . . . . . . . . . . 22.6 Variation of Trap Separation . . . . . . . . . . . . . . . . . . . . . . . . 22.7 Implementation of Qubit Gates . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 287 288 289 290 291 292 293 296 23 Quantum Information Processing with Neutral Atoms on Atom Chips (P. Krüger, A. Haase, M. Andersson, and J. Schmiedmayer) 23.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2 The Atom Chip . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2.1 Combined Magneto–Electric Traps . . . . . . . . . . . . . 23.2.2 RF-induced Adiabatic Potentials for Manipulating Atoms . 23.2.3 Imperfections in the Atom Chip: Disorder Potentials . . . . 23.3 The Qubit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.4 Entangling Qubits . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.4.1 Quantum Gate via Cold Controlled Collisions . . . . . . . . 23.4.2 Motional Qubit Gates with Controlled Collisions . . . . . . 23.5 Input/Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.5.1 Qubit Detection . . . . . . . . . . . . . . . . . . . . . . . . 23.5.2 Quantum Input/Output . . . . . . . . . . . . . . . . . . . . 23.6 Noise and Decoherence . . . . . . . . . . . . . . . . . . . . . . . . 23.7 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 298 298 299 300 301 302 303 303 305 305 305 307 307 308 309 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XII Contents 24 Quantum Gates and Algorithms Operating on Molecular Vibrations (U. Troppmann, C. M. Tesch, and R. de Vivie-Riedle) 24.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24.2 Qubit States Encoded in Molecular Vibrations . . . . . . . . . . . 24.3 Optimal Control Theory for Molecular Dynamics . . . . . . . . . 24.3.1 Local Quantum Gates . . . . . . . . . . . . . . . . . . . 24.4 Multi-target OCT for Global Quantum Gates . . . . . . . . . . . 24.4.1 Global Quantum Gates for Molecular Vibrational Qubits . 24.5 Basis Set Independence and Quantum Algorithms . . . . . . . . . 24.6 Towards More Complex Molecular Systems . . . . . . . . . . . . 24.7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 312 313 313 315 317 317 318 321 324 325 25 Fabrication and Measurement of Aluminum and Niobium Based Single-Electron Transistors and Charge Qubits (W. Krech, D. Born, M. Mihalik, and M. Grajcar) 327 25.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 25.2 Motivation for this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 25.3 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 25.3.1 Scheme of the Junction Preparation Technique . . . . . . . . . . . . 329 25.3.2 Fabrication of Tunnel Devices: SET and Charge Qubit Structures . . 330 25.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 25.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 26 Quantum Dot Circuits for Quantum Computation (R. H. Blick, A. K. Hüttel, A. W. Holleitner, L. Pescini, and H. Lorenz) 26.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26.2 Realizing Quantum Bits in Double Quantum Dots . . . . . . . . 26.3 Controlling the Electron Spin in Single Dots . . . . . . . . . . . 26.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 338 339 346 351 351 27 Manipulation and Control of Individual Photons and Distant Atoms via Linear Optical Elements (X.-B. Zou and W. Mathis) 353 27.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 27.2 Manipulation and Control of Individual Photons via Linear Optical Elements 354 27.2.1 Teleportation Implementation of Non-deterministic NLS Gate and Single-mode Photon Filter . . . . . . . . . . . . . . . . . . . . . . . 354 27.2.2 Implementation of Non-deterministic NLS Gate via Parametric Amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359 27.2.3 Phase Measurement of Light and Generation of Superposition of Fock States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 Contents XIII 27.2.4 Joint Measurement of Photon Number Sum and Phase Difference Operators on a Two-mode Field . . . . . . . . . . . . . . . . . . . . . . 27.2.5 Remark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.3 Quantum Entanglement Between Distant Atoms Trapped in Different Optical Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.3.1 Generation of W States, GHZ States and Cluster States Based on Single-photon Detectors . . . . . . . . . . . . . . . . . . . . . . . . 27.3.2 Generation of W States and GHZ States Based on Four-photon Coincidence Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Conditional Linear Optical Networks (S. Scheel) 28.1 Introduction . . . . . . . . . . . . . . . . 28.2 Measurement-induced Nonlinearities . . . 28.2.1 Beam Splitters and Networks . . . 28.2.2 Post-processing of Single-Photon Detectors . . . . . . . . . . . . . 28.3 Probability of Success and Permanents . . 28.4 Upper Bounds on Success Probabilities . 28.5 Extension Using Weak Nonlinearities . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . and . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Number-Resolving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 370 370 370 376 379 379 382 382 383 384 385 386 388 390 391 29 Multiphoton Entanglement ˙ (M. Bourennane, M. Eibl, S. Gaertner, N. Kiesel, Ch. Kurtsiefer, M. Zukowski, and H. Weinfurter) 393 29.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393 29.2 Entangled Multiphoton State Preparation . . . . . . . . . . . . . . . . . . . . 394 29.3 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 29.4 Quantum Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396 29.5 Bell Inequality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 29.6 Genuine Four-photon Entanglement . . . . . . . . . . . . . . . . . . . . . . 400 29.7 Entanglement Persistence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 29.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403 30 Quantum Polarization for Continuous Variable Information Processing (N. Korolkova) 30.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.2 Nonseparability and Squeezing . . . . . . . . . . . . . . . . . . . . . . 30.2.1 Polarization Squeezing . . . . . . . . . . . . . . . . . . . . . . 30.2.2 Continuous Variable Polarization Entanglement . . . . . . . . . 30.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30.4 Stokes Operators Questioned: Degree of Polarization in Quantum Optics References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 405 406 406 407 410 413 416 XIV 31 A Quantum Optical XOR Gate (H. Becker, K. Schmid, W. Dultz, W. Martienssen, and H. Roskos) 31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Double Bump Photons . . . . . . . . . . . . . . . . . . . 31.3 The XOR Gate . . . . . . . . . . . . . . . . . . . . . . . 31.4 Quad Bump Photons . . . . . . . . . . . . . . . . . . . . 31.5 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418 418 418 420 423 424 424 32 Quantum Fiber Solitons — Generation, Entanglement, and Detection (G. Leuchs, N. Korolkova, O. Glöckl, St. Lorenz, J. Heersink, Ch. Silberhorn, Ch. Marquardt, and U. L. Andersen) 425 32.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 32.2 Quantum Correlations and Entanglement . . . . . . . . . . . . . . . . . . . . 426 32.3 Multimode Quantum Correlations . . . . . . . . . . . . . . . . . . . . . . . 428 32.4 Generation of Bright Entangled Beams . . . . . . . . . . . . . . . . . . . . . 431 32.5 Detection of Entanglement of Bright Beams . . . . . . . . . . . . . . . . . . 432 32.5.1 Sub-shot-noise Phase Quadrature Measurements on Intense Beams . 432 32.5.2 Direct Experimental Test of Non-Separability . . . . . . . . . . . . . 434 32.6 Entanglement Swapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 32.7 Polarization Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439 Index 443 List of Contributors • K. Abich, p. 251 [email protected] • R. Ahlswede, p. 70 [email protected] • G. Alber, p. 14 [email protected] • W. Alt, p. 265 [email protected] • U. Andersen, p. 425 [email protected] • Ch. Balzer, p. 237, p. 251 [email protected] • H. Becker, p. 418 e-mail: see H. Roskos • Th. Beth, p. 1 eiss_offi[email protected] • G. Birkl, p. 287 [email protected] • R.H. Blick, p. 338 [email protected] • D. Born, p. 327 e-mail: see W. Krech • M. Bourennane, p. 393 [email protected] • H.J. Briegel, p. 28 [email protected] • D. Bruß, p. 83 [email protected] • T.C. Bschorr, p. 113 [email protected] • F.B.J. Buchkremer, p. 287 email: see G. Birkl • N. Cai, p. 70 [email protected]atik.uni-bielefeld.de • G. Cennini, p. 275 [email protected] • M. Curty, p. 44 [email protected] • A. Delgado, p. 14 [email protected] • R. de Vivie–Riedle, p. 312 [email protected] • Ch. DiFidio, p. 198 e-mail: see W. Vogel • W. Dultz, p. 418 e-mail: see H. Roskos • R. Dumke, p. 287 e-mail: see W. Ertmer • K. Eckert, p. 83 [email protected] • M. Eibl, p. 393 [email protected] Preface to the First Edition The Senate of the German Research Council (Deutsche Forschungsgemeinschaft) has set up a Focused Research Program “Quantum Information Processing” in July 1998. The Focused Program was jointly initiated by Th. Beth, G. Leuchs, W. Mathis, and W. Schleich. The present volume surveys the results of this work during the years 1999–2002. The main thrive of this Focused Program is the research of the foundations of quantum information processing by means of controlled manipulation of entangled states. First experiments show that one can generate entangled states in a controlled way and manipulate them to a certain extent. This progress was made possible due to the recently developing unique worldwide synergy between theoretical and experimental physics, computer sciences, telecommunications and mathematics in the field of so called quantum information and physics of computation founded by Feynman. The goal of this interdisciplinary Focused Program “Quantum Information Processing” is the systematic investigation of quantum systems aimed at their exact theoretical modelling and experimental manipulation, at tests of the foundations of quantum information and quantum physics and at the applications in the computer sciences, telecommunication, cryptography and high-precision measurement, quantum-error control and switching technologies. The main goal is meant to be not the examination of systems using quantum mechanical methods, as for example in the case of spectroscopy, but merely the controlled manipulation and exploitation of entangled states. The development of some fields of modern physics leads to the possibility to isolate and to control quantum phenomena ever better. The transfer of the properties of a quantum state over a silica fibre, the high-precision backaction-evading, partially even interaction- free, measurements and the “computation” with quantum state are examples for that. All this is based on the principles of the state superposition and entanglement of various systems. The dream of a successful solution of exponentially difficult computational problems, like optimization or pattern identification could be thus fulfilled, despite of limited material hardware resources. According to general considerations these problems cannot be handled by means of classical computers with reasonable success chances. Entangled states have played an important role in the attempt to understand quantum phenomena in Gedanken-experiments already at the beginning of quantum physics. This topic has surfaced again due to novel possibilities for the actual implementation of these Gedankenexperiments by means of modern physics. The new experiments on the foundations of physics provide more and more demanding tests of the quantum theory and the question of nonlocality. In the last 7 years new surprising effects were discovered in this field. A spectacular example of such effects is teleportation making use of the non-locality of entangled states to XVI Preface transfer the properties of a quantum state or the possibility of a truly exponential speed-up of quantum algorithms over classical algorithms. Apart from this, there are some recent suggestions to employ the specific features of quantum information for technological applications. Such as quantum key distribution and the use of multipartite entanglement in quantum communication protocols. Recent discoveries on the information-theoretical side suggest that new surprising applications be provided by such technologies still to be invented – exceeding the state of today’s Quantum Key Exchange apparatus. One main goal is to construct a highly parallel computer which works according to a completely new paradigm and which in all probability can solve problems, which are not efficiently solvable with a conventional computer. Further applications open up in optical communication and in cryptographic key distribution. The exploitation of the entanglement to be studied here is developing into an important concept. It is the basis for the effects of acceleration and precision predicted by theory. It is hoped that the results and perception gained from the studies of pure demonstration systems in the frame of this program will help to increase the know-how required towards building future industrial products such as a quantum processing machine. Delimitation from other Quantum Mechanical Problems: The further optimization of the up-to-date CMOS-Technology is expected to be completed in fifteen years at the latest. All the alternatives to CMOS-Technology (e.g. single electron transistor (SET), resonant tunneling devices (RTD), rapid single flux quantum devices (RSFQ), molecular nanoelectronics (ME) and spin-devices/magneto-electronics (SD)) recognizable today are based on quantum phenomena. However they do not make use of the entanglement principle. This eliminates the advantage of the exponential gain via scalable entangled pure quantum states provided by quantum information processing. In a similar way the goals of the quantum information processing differ from the methods of NMR- and laser spectroscopy. The main goal of spectroscopy is to examine an unknown system (for example a molecule or a solid) making use of quantum mechanical phenomena. Quantum information processing in contrast abstracts first from the system itself. The subject of this Focused Program is the research and controlled exploitation of the fundamental quantum mechanical effects in pure, experimentally realizable systems, keeping in mind the technical feasibility. All the applications have been judged accordingly. General experimental or theoretical investigations to e.g. the foundations of quantum mechanics without direct connection are not part of the focused program. The contributed chapters in this volume are grouped according to the following list of topics: • quantum algorithms and modelling and construction of elementary quantum logic elements and gates • theoretical studies of the exploitation of quantum information and entanglement, as well as of their quantification • analysis and control of the decoherence in quantum systems • experimental realization of the controlled entangled quantum states in as pure as possible, well modelled systems • quantum communication and cryptography Preface XVII The most recent results of the Schwerpunktprogramm can be found by calling the home page http://www.quiv.de. On behalf of all participants of the Schwerpunktprogramm we gratefully acknowledge the long term funding of this research project by the Deutsche Forschungsgemeinschaft (DFG). We are especially indebted to Dr. A. Szillinsky, Dr. A. Engelke, Dr. K. Wefelmeier, and Dr. S. Krückeberg for their guidance during the development and the pursuit of this research programme. For the first renewal of the research projects there was an unforeseen large number of applications. We are most grateful to the Bundesministerium für Bildung und Forschung for helping with additional funding through its VDI-office and we especially thank Dr. M. Böltau for his support. We express our sincere thanks to Gerlinde Gardavsky, Dr. Markus Grassl, Priv. Doz. Dr. Natalia Korolkova, Christoph Marquardt, Dr. Martin Rötteler, Jessica Schneider, and Robert Zeier for their help during the preparation of this volume. Thomas Beth and Gerd Leuchs October 2002 Preface to the Second Edition Since the publication of the first edition the results extensively described there have become established knowledge in Quantum Information Processing. Beyond this, new directions of research have evolved from amongst these areas. Thus in addition to revised chapters of the first edition, this second edition contains the additional new chapters 4, 12, 13, 24, 27–30 and 32. The editors are pleased to note that the support for quantum information has been increasing during these last two years within Germany. The Deutsche Forschungsgemeinschaft is now funding a Graduiertenkolleg in Dortmund and a Sonderforschungsbereich in München. In addition several of the groups contributing to this volume received funding from the project “Quantum Information Highway A8” which is jointly sponsored by the Landesstiftung BadenWürtemberg GmbH and the Bayerisches Staatsministerium für Forschung, Wissenschaft und Kunst. Our community is most grateful for this support and the present volume displays a cross section of the funded work. Gerd Leuchs and Thomas Beth November 2004

Author Gerd Leuchs and Thomas Beth Isbn 9783527405411 File size 41.26MB Year 2005 Pages 471 Language English File format PDF Category Physics Book Description: FacebookTwitterGoogle+TumblrDiggMySpaceShare Quantum processing and communication is emerging as a challenging technique at the beginning of the new millennium. This is an up-to-date insight into the current research of quantum superposition, entanglement, and the quantum measurement process – the key ingredients of quantum information processing. The authors further address quantum protocols and algorithms. Complementary to similar programmes in other countries and at the European level, the German Research Foundation (DFG) realized a focused research program on quantum information. The contributions – written by leading experts – bring together the latest results in quantum information as well as addressing all the relevant questions.     Download (41.26MB) Earthquake Prediction With Radio Techniques Quantum Information in Gravitational Fields Quantum Systems, Channels, Information: A Mathematical Introduction Introduction to Quantum Theory Quantum Mechanics Ii: Advanced Topics Load more posts

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