Details

Quantum Information

From Foundations to Quantum Technology Applications
2. Aufl.

von: Dagmar Bruss, Gerd Leuchs
282,99 €
Verlag:	Wiley-VCH
Format:	EPUB
Veröffentl.:	05.02.2019
ISBN/EAN:	9783527805792
Sprache:	englisch
Anzahl Seiten:	512

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Beschreibungen

Titelbeschreibung

This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. It contains problems and exercises and is therefore ideally suited for students and lecturers in physics and informatics, as well as experimental and theoretical physicists in academia and industry who work in the field of quantum information processing. The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.

Inhaltsverzeichnis

Preface to the New Edition xvii Preface to Lectures on Quantum Information (2006) xix Part I Classical Information Theory 1 1 Classical Information Theory and Classical Error Correction 3 Markus Grassl 1.1 Introduction 3 1.2 Basics of Classical Information Theory 3 1.3 Linear Block Codes 10 1.4 Further Aspects 16 References 16 2 Computational Complexity 19 Stephan Mertens 2.1 Basics 19 2.2 Algorithms and Time Complexity 21 2.3 Tractable Trails: The Class P 22 2.4 Intractable Itineraries: The Class NP 24 2.5 Reductions and NP-Completeness 29 2.6 P Versus NP 31 2.7 Optimization 34 2.8 Complexity Zoo 37 References 37 Part II Foundations of Quantum Information Theory 39 3 Discrete Quantum States versus Continuous Variables 41 Jens Eisert 3.1 Introduction 41 3.2 Finite-Dimensional Quantum Systems 42 3.3 Continuous-Variables 45 References 53 4 Approximate Quantum Cloning 55 Dagmar Bruß and Chiara Macchiavello 4.1 Introduction 55 4.2 The No-Cloning Theorem 56 4.3 State-Dependent Cloning 57 4.4 Phase-Covariant Cloning 63 4.5 Universal Cloning 65 4.6 Asymmetric Cloning 69 4.7 Probabilistic Cloning 70 4.8 Experimental Quantum Cloning 70 4.9 Summary and Outlook 71 Exercises 72 References 73 5 Channels and Maps 75 M. Keyl and R. F.Werner 5.1 Introduction 75 5.2 Completely Positive Maps 75 5.3 The Choi–Jamiolkowski Isomorphism 78 5.4 The Stinespring Dilation Theorem 80 5.5 Classical Systems as a Special Case 83 5.6 Channels with Memory 84 5.7 Examples 86 Problems 89 References 90 6 Quantum Algorithms 91 Julia Kempe 6.1 Introduction 91 6.2 Precursors 93 6.3 Shor’s Factoring Algorithm 97 6.4 Grover’s Algorithm 100 6.5 Other Algorithms 101 6.6 Recent Developments 103 Exercises 105 References 106 7 Quantum Error Correction 111 Markus Grassl 7.1 Introduction 111 7.2 Quantum Channels 111 7.3 Using Classical Error-Correcting Codes 115 7.4 Further Aspects 124 References 124 Part III Theory of Entanglement 127 8 The Separability versus Entanglement Problem 129 Sreetama Das, Titas Chanda,Maciej Lewenstein, Anna Sanpera, Aditi Sen De, and Ujjwal Sen 8.1 Introduction 129 8.2 Bipartite Pure States: Schmidt Decomposition 130 8.3 Bipartite Mixed States: Separable and Entangled States 131 8.4 Operational Entanglement Criteria 132 8.5 Non-operational Entanglement Criteria 141 8.5.1 Technical Preface 141 8.6 Bell Inequalities 149 8.7 Quantification of Entanglement 152 8.8 Classification of Bipartite States with Respect to Quantum Dense Coding 158 8.9 Multipartite States 162 Exercises 167 Acknowledgments 168 References 169 9 Quantum Discord and Nonclassical Correlations Beyond Entanglement 175 Gerardo Adesso, Marco Cianciaruso, and Thomas R. Bromley 9.1 Introduction 175 9.2 Quantumness Versus Classicality (of Correlations) 176 9.3 Quantifying Quantum Correlations – Quantum Discord 180 9.4 Interpreting Quantum Correlations – Local Broadcasting 184 9.5 Alternative Characterizations of Quantum Correlations 186 9.6 General Desiderata for Measures of Quantum Correlations 190 9.7 Outlook 191 Exercises 191 References 192 10 Entanglement Theory with Continuous Variables 195 Peter van Loock and Evgeny Shchukin 10.1 Introduction 195 10.2 Phase-Space Description 197 10.3 Entanglement of Gaussian States 197 10.4 More on Gaussian Entanglement 209 Exercises 211 References 212 11 Entanglement Measures 215 Martin B. Plenio and Shashank S. Virmani 11.1 Introduction 215 11.2 Manipulation of Single Systems 217 11.3 Manipulation in the Asymptotic Limit 218 11.4 Postulates for Axiomatic Entanglement Measures: Uniqueness and Extremality Theorems 221 11.5 Examples of Axiomatic Entanglement Measures 224 Acknowledgments 228 References 228 12 Purification and Distillation 231 Wolfgang Dür and Hans-J. Briegel 12.1 Introduction 231 12.2 Pure States 233 12.3 Distillability and Bound Entanglement in Bipartite Systems 235 12.4 Bipartite Entanglement Distillation Protocols 239 12.5 Distillability and Bound Entanglement in Multipartite Systems 247 12.6 Entanglement Purification Protocols in Multipartite Systems 248 12.7 Distillability with Noisy Apparatus 252 12.8 Applications of Entanglement Purification 257 12.9 Summary and Conclusions 260 Acknowledgments 261 References 261 13 Bound Entanglement 265 Paweł Horodecki 13.1 Introduction 265 13.2 Distillation of Quantum Entanglement: Repetition 265 13.3 Bound Entanglement – Bipartite Case 269 13.4 Bound Entanglement: Multipartite Case 282 13.5 Further Reading: Continuous Variables 287 Exercises 287 References 288 14 Multipartite Entanglement 293 Michael Walter, David Gross, and Jens Eisert 14.1 Introduction 293 14.2 General Theory 294 14.3 Important Classes of Multipartite states 310 14.4 Specialized Topics 316 Acknowledgments 321 References 321 Part IV Quantum Communication 331 15 Quantum Teleportation 333 Natalia Korolkova 15.1 Introduction 333 15.2 Quantum Teleportation Protocol 334 15.3 Implementations 340 References 349 16 Theory of Quantum Key Distribution (QKD) 353 Norbert Lütkenhaus 16.1 Introduction 353 16.2 Classical Background to QKD 353 16.3 Ideal QKD 354 16.4 Idealized QKD in Noisy Environment 357 16.5 Realistic QKD in Noisy and Lossy Environment 360 16.6 Improved Schemes 363 16.7 Improvements in Public Discussion 364 16.8 Conclusion 365 References 365 17 Quantum Communication Experiments with Discrete Variables 369 Harald Weinfurter 17.1 Aunt Martha 369 17.2 Quantum Cryptography 369 17.3 Entanglement-Based Quantum Communication 375 17.4 Conclusion 379 References 379 18 Continuous Variable Quantum Communication with Gaussian States 383 Ulrik L. Andersen and Gerd Leuchs 18.1 Introduction 383 18.2 Continuous-Variable Quantum Systems 384 18.3 Tools for State Manipulation 386 18.4 Quantum Communication Protocols 391 Exercises 397 References 397 Part V Quantum Computing: Concepts 401 19 Requirements for a Quantum Computer 403 Artur Ekert and Alastair Kay 19.1 Classical World of Bits and Probabilities 403 19.2 Logically Impossible Operations? 408 19.3 Quantum World of Probability Amplitudes 410 19.4 Interference Revisited 414 19.5 Tools of the Trade 416 19.6 Composite Systems 422 19.7 Quantum Circuits 428 19.8 Summary 433 Exercises 433 20 Probabilistic Quantum Computation and Linear Optical Realizations 437 Norbert Lütkenhaus 20.1 Introduction 437 20.2 Gottesman/Chuang Trick 438 20.3 Optical Background 439 20.4 Knill–Laflamme–Milburn (KLM) Scheme 441 References 446 21 One-Way Quantum Computation 449 Dan Browne and Hans Briegel 21.1 Introduction 449 21.2 Simple Examples 451 21.3 Beyond Quantum Circuit Simulation 455 21.4 Implementations 465 21.5 Recent Developments 466 21.6 Outlook 469 Acknowledgments 469 Exercises 469 References 470 22 Holonomic Quantum Computation 475 Angelo C. M. Carollo and Vlatko Vedral 22.1 Geometric Phase and Holonomy 475 22.2 Application to Quantum Computation 479 References 480 Part VI Quantum Computing: Implementations 483 23 Quantum Computing with Cold Ions and Atoms: Theory 485 Dieter Jaksch, Juan José García-Ripoll, Juan Ignacio Cirac, and Peter Zoller 23.1 Introduction 485 23.2 Trapped Ions 485 23.3 Trapped Neutral Atoms 495 References 515 24 Quantum Computing Experiments with Cold Trapped Ions 519 Ferdinand Schmidt-Kaler and Ulrich Poschinger 24.1 Introduction to Trapped-Ion Quantum Computing 519 24.2 Paul Traps 522 24.3 Ion Crystals and Normal Modes 526 24.4 Trap Technology 529 Acknowledgements 547 References 547 25 Quantum Computing with Solid-State Systems 553 Guido Burkard and Daniel Loss 25.1 Introduction 553 25.2 Concepts 554 25.3 Electron Spin Qubits 563 25.4 Superconducting Qubits 575 References 583 26 Time-Multiplexed Networks for Quantum Optics 587 Sonja Barkhofen, Linda Sansoni and Christine Silberhorn 26.1 Introduction 587 26.2 Multiplexing 588 26.3 Photon-Number-Resolving Detection with Time Multiplexing 589 26.4 Quantum Walks in Time 592 26.5 Conclusion 600 References 601 27 A Brief on Quantum Systems Theory and Control Engineering 607 Thomas Schulte-Herbrüggen, Robert Zeier,Michael Keyl, and Gunther Dirr 27.1 Introduction 607 27.2 Systems Theory of Closed Quantum Systems 609 27.3 Toward a Systems Theory for Open Quantum Systems 620 27.4 Relation to Numerical Optimal Control 624 27.5 Outlook on Infinite-Dimensional Systems 626 27.6 Conclusion 633 Acknowledgments 633 Exercises 634 References 635 28 Quantum Computing Implemented via Optimal Control: Application to Spin and Pseudospin Systems 643 Thomas Schulte-Herbrüggen, Andreas Spörl, Raimund Marx, Navin Khaneja, JohnMyers, Amr Fahmy, Samuel Lomonaco, Louis Kauffman, and Steffen Glaser 28.1 Introduction 643 28.2 From Controllable Spin Systems to Suitable Molecules 645 28.3 Scalability 647 28.4 Algorithmic Platform for Quantum Control Systems 649 28.5 Applied Quantum Control 651 28.6 Worked Example: Unitary Controls for Classifying Knots by NMR 656 28.7 Conclusions 661 Acknowledgments 662 Exercises 662 References 663 Part VII Quantum Interfaces and Memories 669 29 Cavity Quantum Electrodynamics: Quantum Information Processing with Atoms and Photons 671 Jean-Michel Raimond and Gerhard Rempe 29.1 Introduction 671 29.2 Microwave Cavity Quantum Electrodynamics 672 29.3 Optical Cavity Quantum Electrodynamics 677 29.4 Conclusions and Outlook 683 References 684 30 Quantum Repeater 691 Wolfgang Dür, Hans-J. Briegel, Peter Zoller, and Peter v Loock 30.1 Introduction 691 30.2 Concept of the Quantum Repeater 693 30.3 Proposals for Experimental Realization 697 30.4 Summary and Conclusions 699 Acknowledgments 699 References 699 31 Quantum Interface Between Light and Atomic Ensembles 701 Eugene S. Polzik and Jaromír Fiurášek 31.1 Introduction 701 31.2 Off-Resonant Interaction of Light with Atomic Ensemble 702 31.3 Entanglement of Two Atomic Clouds 711 31.4 Quantum Memory for Light 712 31.5 Multiple Passage Protocols 715 31.6 Atoms-Light Teleportation and Entanglement Swapping 718 31.7 Quantum Cloning into Atomic Memory 720 31.8 Summary 721 Acknowledgment 721 References 721 32 Echo-Based Quantum Memory 723 G. T. Campbell, K. R. Ferguson, M. J. Sellars, B. C. Buchler, and P. K. Lam 32.1 Overview of Photon Echo Techniques 724 32.2 Platforms for Echo-Based Quantum Memory 728 32.3 Characterization 731 32.4 Demonstrations 734 32.5 Outlook 736 References 737 33 Quantum Electrodynamics of a Qubit 741 Gernot Alber and Georgios M. Nikolopoulos 33.1 Quantum Electrodynamics of a Qubit in a Spherical Cavity 742 33.2 Suppression of Radiative Decay of a Qubit in a Photonic Crystal 750 Exercises 755 References 756 34 Elementary Multiphoton Processes in Multimode Scenarios 759 Nils Trautmann and Gernot Alber 34.1 A Generic Quantum Electrodynamical Model 761 34.2 The Multiphoton Path Representation 761 34.3 Examples 767 34.4 Conclusion 772 Appendix A: Evaluation of the Field Commutator 773 References 774 Part VIII Towards Quantum Technology Applications 777 35 Quantum Interferometry with Gaussian States 779 Ulrik L. Andersen, Oliver Glöckl, Tobias Gehring, and Gerd Leuchs 35.1 Introduction 779 35.2 The Interferometer 780 35.3 Interferometer with Coherent States of Light 783 35.4 Interferometer with Squeezed States of Light 786 35.5 Fundamental Limits 792 35.6 Summary and Discussion 793 Problems 795 References 796 36 Quantum Logic-Enabled Spectroscopy 799 Piet O. Schmidt 36.1 Introduction 799 36.2 Trapping and Doppler Cooling of a Two-Ion Crystal 800 36.3 Coherent Atom–Light Interaction and State Manipulation 802 36.4 Quantum Logic Spectroscopy for Optical Clocks 805 36.5 Photon Recoil Spectroscopy 809 36.6 Quantum Logic with Molecular Ions 815 36.7 Nonclassical States for Spectroscopy 819 36.8 Future Directions 821 Acknowledgments 822 References 822 37 Quantum Imaging 827 Claude Fabre and Nicolas Treps 37.1 Introduction 827 37.2 The Quantum Laser Pointer 828 37.3 Manipulation of Spatial Quantum Noise 830 37.4 Two-Photon Imaging 832 37.5 Other Topics in Quantum Imaging 833 37.6 Conclusion and Perspectives 834 Acknowledgment 835 References 835 38 Quantum Frequency Combs 837 Claude Fabre and Nicolas Treps 38.1 Introduction 837 38.2 Parametric Down Conversion of a Frequency Comb 839 38.3 Experiment 840 38.4 Experimental Results 843 38.5 Application to Quantum Information Processing 849 38.6 Application to Quantum Metrology 853 38.7 Conclusion 854 Acknowledgment 855 References 855 Index 859

Autorenportrait

Dagmar Bru? graduated at RWTH University Aachen, Germany, and received her PhD in theoretical particle physics from the University of Heidelberg in 1994. As a research fellow at the University of Oxford she became interested in quantum information. Another European fellowship at ISI Torino, Italy, followed. While being a research assistant at the University of Hannover she completed her habilitation. Since 2004 Professor Bru? has been holding a chair at the Institute of Theoretical Physics at Heinrich-Heine-University Dusseldorf, Germany. Her research pertains to theoretical aspects of quantum information processing. Gerd Leuchs studied physics and mathematics at the University of Cologne, Germany, and received his Ph.D. in 1978. After two years at the University of Colorado in Boulder, USA, he headed the German gravitational wave detection group from 1985 to 1989. He became technical director at Nanomach AG in Switzerland. Since 1994 Professor Leuchs has been holding the chair for optics at the University of Erlangen-Nuremberg, Germany. In 2009 he was a founding director of the Max Planck Institute for the Science of Light. He is visiting professor at the University of Ottawa. His fields of research span the range from modern aspects of classical optics to quantum optics and quantum information.

Back cover copy

This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. It contains problems and exercises and is therefore ideally suited for students and lecturers in physics and informatics, as well as experimental and theoretical physicists in academia and industry who work in the field of quantum information processing. The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.