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Quantum Information Vital Source e-bog
Dagmar Bruss
(2019)
John Wiley & Sons
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Quantum Information, 2 Volume Set
From Foundations to Quantum Technology Applications
Dagmar Bruss og Gerd Leuchs
(2019)
Sprog: Engelsk
John Wiley & Sons, Incorporated
3.555,00 kr.
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Detaljer om varen
- 1. Udgave
- Vital Source searchable e-book (Reflowable pages)
- Udgiver: John Wiley & Sons (Februar 2019)
- ISBN: 9783527805792
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.
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Detaljer om varen
- 2. Udgave
- Hardback: 512 sider
- Udgiver: John Wiley & Sons, Incorporated (Juni 2019)
- Forfattere: Dagmar Bruss og Gerd Leuchs
- ISBN: 9783527413539
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.
The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.
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 Pawel 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 Schul
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 Pawel 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 Schul
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