Quantum information theory:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 655 S. Ill., graph. Darst. |
| ISBN: | 9781107034259 |
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Record in the Search Index
| _version_ | 1804149509931925504 |
|---|---|
| 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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| dewey-full | 535.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535.15 |
| dewey-search | 535.15 |
| dewey-sort | 3535.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik |
| edition | 1. publ. |
| format | Book |
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| spelling | Wilde, Mark M. 1980- Verfasser (DE-588)1035349086 aut Quantum information theory Mark M. Wilde 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XV, 655 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Informationstheorie (DE-588)4026927-9 gnd rswk-swf Quantenkommunikation (DE-588)4596977-2 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantentheorie (DE-588)4047992-4 s Informationstheorie (DE-588)4026927-9 s DE-604 Quanteninformatik (DE-588)4705961-8 s Quantenkommunikation (DE-588)4596977-2 s 1\p DE-604 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| 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 |
| topic_facet | Informationstheorie Quantenkommunikation Quanteninformatik Quantentheorie |
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