Verfügbarkeit: Quantum information theory | Technische Universität München

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Bibliographische Detailangaben
Beteilige Person:	Wilde, Mark M. 1980- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2013
Ausgabe:	1. publ.
Schlagwörter:	Informationstheorie Quantenkommunikation Quanteninformatik Quantentheorie
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025297283&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XV, 655 S. Ill., graph. Darst.
ISBN:	9781107034259

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Datensatz im Suchindex

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adam_text	Titel: Quantum information theory Autor: Wilde, Mark M Jahr: 2013 Contents How To Use This Book page xi Acknowledgments xiv Part I Introduction 1 1 Concepts in Quantum Shannon Theory 3 1.1 Overview of the Quantum Theory 7 1.2 The Emergence of Quantum Shannon Theory 11 2 Classical Shannon Theory 26 2.1 Data Compression 26 2.2 Channel Capacity 35 2.3 Summary 49 Part II The Quantum Theory 51 3 The Noiseless Quantum Theory 53 3.1 Overview 54 3.2 Quantum Bits 55 3.3 Reversible Evolution 61 3.4 Measurement 68 3.5 Composite Quantum Systems 74 3.6 Summary and Extensions to Qudit States 89 3.7 History and Further Reading 96 4 The Noisy Quantum Theory 97 4.1 Noisy Quantum States 98 4.2 Measurement in the Noisy Quantum Theory 110 4.3 Composite Noisy Quantum Systems 112 4.4 Noisy Evolution 120 4.5 Summary 139 4.6 History and Fürther Reading 140 5 The Purified Quantum Theory 141 5.1 Purification 142 5.2 Isometric Evolution 143 Contents 5.3 Coherent Quantum Instrument 154 5.4 Coherent Measurement 155 5.5 History and Further Reading 156 Part III Unit Quantum Protocols 157 6 Three Unit Quantum Protocols 159 6.1 Non-local Unit Resources 160 6.2 Protocols 162 6.3 Optimality of the Three Unit Protocols 171 6.4 Extensions for Quantum Shannon Theory 173 6.5 Three Unit Qudit Protocols 174 6.6 History and Further Reading 180 7 Coherent Protocols 181 7.1 Definition of Coherent Communication 182 7.2 Implementations of a Coherent Bit Channel 184 7.3 Coherent Dense Coding 185 7.4 Coherent Teleportation 187 7.5 The Coherent Communication Identity 189 7.6 History and Further Reading 190 8 The Unit Resource Capacity Region 191 8.1 The Unit Resource Achievable Region 191 8.2 The Direct Coding Theorem 195 8.3 The Converse Theorem 196 8.4 History and Further Reading 200 Part IV Tools of Quantum Shannon Theory 201 9 Distance Measures 203 9.1 Trace Distance 204 9.2 Fidelity 212 9.3 Relationships between Trace Distance and Fidelity 219 9.4 Gentle Measurement 223 9.5 Fidelity of a Noisy Quantum Channel 226 9.6 The Hilbert-Schmidt Distance Measure 230 9.7 History and Further Reading 231 10 Classical Information and Entropy 232 10.1 Entropy of a Random Variable 233 10.2 Conditional Entropy 237 10.3 Joint Entropy 239 10.4 Mutual Information 239 10.5 Relative Entropy 240 Contents VII 10.6 Conditional Mutual Information 241 10.7 Information Inequalities 243 10.8 Classical Information and Entropy of Quantum Systems 249 10.9 History and Further Reading 251 11 Quantum Information and Entropy 252 11.1 Quantum Entropy 253 11.2 Joint Quantum Entropy 258 11.3 Potential yet Unsatisfactory Definitions of Conditional Quantum Entropy 261 11.4 Conditional Quantum Entropy 263 11.5 Coherent Information 265 11.6 Quantum Mutual Information 267 11.7 Conditional Quantum Mutual Information 270 11.8 Quantum Relative Entropy 272 11.9 Quantum Information Inequalities 275 11.10 History and Further Reading 290 12 The Information of Quantum Channels 292 12.1 Mutual Information of a Classical Channel 293 12.2 Private Information of a Wiretap Channel 299 12.3 Holevo Information of a Quantum Channel 303 12.4 Mutual Information of a Quantum Channel 309 12.5 Coherent Information of a Quantum Channel 314 12.6 Private Information of a Quantum Channel 319 12.7 Summary 325 12.8 History and Further Reading 326 13 Classical Typicality 327 13.1 An Example of Typicality 328 13.2 Weak Typicality 329 13.3 Properties of the Typical Set 331 13.4 Application of Typical Sequences: Shannon Compression 333 13.5 Weak Joint Typicality 335 13.6 Weak Conditional Typicality 338 13.7 Strong Typicality 341 13.8 Strong Joint Typicality 350 13.9 Strong Conditional Typicality 352 13.10 Application: Shannon s Channel Capacity Theorem 358 13.11 Concluding Remarks 362 13.12 History and Further Reading 363 14 Quantum Typicality 364 14.1 The Typical Subspace 365 14.2 Conditional Quantum Typicality 375 viii Contents 14.3 The Method of Types for Quantum Systems 384 14.4 Concluding Remarks 387 14.5 History and Further Reading 387 15 The Packing Lemma 388 15.1 Introductory Example 389 15.2 The Setting of the Packing Lemma 389 15.3 Statement of the Packing Lemma 391 15.4 Proof of the Packing Lemma 393 15.5 Derandomization and Expurgation 398 15.6 History and Further Reading 400 16 The Covering Lemma 401 16.1 Introductory Example 402 16.2 Setting and Statement of the Covering Lemma 404 16.3 Proof of the Covering Lemma 406 16.4 History and Further Reading 413 Part V Noiseless Quantum Shannon Theory 415 17 Schumacher Compression 417 17.1 The Information-Processing Task 418 17.2 The Quantum Data-Compression Theorem 420 17.3 Quantum Compression Example 424 17.4 Variations on the Schumacher Theme 425 17.5 Concluding Remarks 427 17.6 History and Further Reading 427 18 Entanglement Concentration 429 18.1 An Example of Entanglement Concentration 430 18.2 The Information-Processing Task 433 18.3 The Entanglement Concentration Theorem 433 18.4 Common Randomness Concentration 440 18.5 Schumacher Compression versus Entanglement Concentration 441 18.6 Concluding Remarks 445 18.7 History and Further Reading 445 Part VI Noisy Quantum Shannon Theory 447 19 Classical Communication 451 19.1 Naive Approach: Product Measurements at the Decoder 453 19.2 The Information-Processing Task 456 19.3 The Classical Capacity Theorem 458 19.4 Examples of Channels 463 Contents 19.5 Superadditivity of the Holevo Information 471 19.6 Concluding Remarks 474 19.7 History and Further Reading 475 20 Entanglement-Assisted Classical Communication 477 20.1 The Information-Processing Task 479 20.2 A Preliminary Example 480 20.3 The Entanglement-Assisted Classical Capacity Theorem 484 20.4 The Direct Coding Theorem 484 20.5 The Converse Theorem 493 20.6 Examples of Channels 501 20.7 Concluding Remarks 506 20.8 History and Further Reading 507 21 Coherent Communication with Noisy Resources 508 21.1 Entanglement-Assisted Quantum Communication 509 21.2 Quantum Communication 514 21.3 Noisy Super-Dense Coding 515 21.4 State Transfer 518 21.5 Trade-off Coding 522 21.6 Concluding Remarks 530 21.7 History and Further Reading 531 22 Private Classical Communication 532 22.1 The Information-Processing Task 533 22.2 The Private Classical Capacity Theorem 536 22.3 The Direct Coding Theorem 536 22.4 The Converse Theorem 545 22.5 Discussion of Private Classical Capacity 546 22.6 History and Further Reading 549 23 Quantum Communication 550 23.1 The Information-Processing Task 551 23.2 The No-Cloning Theorem and Quantum Communication 553 23.3 The Quantum Capacity Theorem 554 23.4 The Direct Coding Theorem 555 23.5 Converse Theorem 562 23.6 An Interlude with Quantum Stabilizer Codes 564 23.7 Example Channels 571 23.8 Discussion of Quantum Capacity 574 23.9 Entanglement Distillation 579 23.10 History and Further Reading 582 Contents 24 Trading Resources for Communication 585 24.1 The Information-Processing Task 586 24.2 The Quantum Dynamic Capacity Theorem 588 24.3 The Direct Coding Theorem 593 24.4 The Converse Theorem 596 24.5 Examples of Channels 606 24.6 History and Further Reading 616 25 Summary and Outlook 618 25.1 Unit Protocols 619 25.2 Noiseless Quantum Shannon Theory 619 25.3 Noisy Quantum Shannon Theory 620 25.4 Protocols Not Covered in This Book 623 25.5 Network Quantum Shannon Theory 624 25.6 Future Directions 625 Appendix A Miscellaneous Mathematics 626 Appendix B Monotonicity of Quantum Relative Entropy 633 References 639 Index 653
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spellingShingle	Wilde, Mark M. 1980- Quantum information theory Informationstheorie (DE-588)4026927-9 gnd Quantenkommunikation (DE-588)4596977-2 gnd Quanteninformatik (DE-588)4705961-8 gnd Quantentheorie (DE-588)4047992-4 gnd
subject_GND	(DE-588)4026927-9 (DE-588)4596977-2 (DE-588)4705961-8 (DE-588)4047992-4
title	Quantum information theory
title_auth	Quantum information theory
title_exact_search	Quantum information theory
title_full	Quantum information theory Mark M. Wilde
title_fullStr	Quantum information theory Mark M. Wilde
title_full_unstemmed	Quantum information theory Mark M. Wilde
title_short	Quantum information theory
title_sort	quantum information theory
topic	Informationstheorie (DE-588)4026927-9 gnd Quantenkommunikation (DE-588)4596977-2 gnd Quanteninformatik (DE-588)4705961-8 gnd Quantentheorie (DE-588)4047992-4 gnd
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