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E-raamat: Quantum Information Theory

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(Louisiana State University)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Apr-2013
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781107070233
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Quantum Information TheorySuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Apr-2013
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781107070233
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"Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject 'from the ground up' it covers classical results as well as major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quantum information theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo information, and the superactivation of quantum capacity. This book will be warmly welcomed by the upcoming generation of quantum information theorists and the already established communityof classical information theorists"--

A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.

Arvustused

' a modern self-contained text suitable for graduate-level courses leading up to research level.' Journal of Discrete Mathematical Sciences and Cryptography 'Mark M. Wilde's Quantum Information Theory is a natural expositor's labor of love. Accessible to anyone comfortable with linear algebra and elementary probability theory, Wilde's book brings the reader to the forefront of research in the quantum generalization of Shannon's information theory. What had been a gaping hole in the literature has been replaced by an airy edifice, scalable with the application of reasonable effort and complete with fine vistas of the landscape below.' Patrick Hayden, Stanford University, California ' the book does a phenomenal job of introducing, developing and nurturing a mathematical sense of quantum information processing In a nutshell, this is an essential reference for students and researchers who work in the area or are trying to understand what it is that quantum information theorists study. Wilde, as mentioned in his book, beautifully illustrates 'the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations' through this book. I would strongly recommend it to anyone who plans to continue working in the field of quantum information.' Subhayan Roy Moulick, SIGCAT News 'During the four years after the appearance of the first edition the author collected misprints and suggestions he got from colleges who used this book to prepare their lectures as well as other readers to brush up verbal formulations and formal notations for the present edition. He also got ideas to do so giving himself courses on this topic in the meantime. The character and main contents of this book did not change and are well described by the reviewer of the first edition. The number of exercises has been enlarged, the discussions about Bell's theorem and the CHSH developments have been enlarged as well as the representation of the theory of quantum channels. Proofs of entropy inequalities, and the dynamics of erasure processes have been added. The present edition includes the important developments of the latter years.' K.-E. Hellwig, Zentralblatt MATH

Muu info

Short-listed for PROSE Award for Computing and Information Sciences 2013.A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.
How To Use This Book xi
Acknowledgments xiv
Part I Introduction
1(50)
1 Concepts in Quantum Shannon Theory
3(23)
1.1 Overview of the Quantum Theory
7(4)
1.2 The Emergence of Quantum Shannon Theory
11(15)
2 Classical Shannon Theory
26(25)
2.1 Data Compression
26(9)
2.2 Channel Capacity
35(14)
2.3 Summary
49(2)
Part II The Quantum Theory
51(106)
3 The Noiseless Quantum Theory
53(44)
3.1 Overview
54(1)
3.2 Quantum Bits
55(6)
3.3 Reversible Evolution
61(7)
3.4 Measurement
68(6)
3.5 Composite Quantum Systems
74(15)
3.6 Summary and Extensions to Qudit States
89(7)
3.7 History and Further Reading
96(1)
4 The Noisy Quantum Theory
97(44)
4.1 Noisy Quantum States
98(12)
4.2 Measurement in the Noisy Quantum Theory
110(2)
4.3 Composite Noisy Quantum Systems
112(8)
4.4 Noisy Evolution
120(19)
4.5 Summary
139(1)
4.6 History and Further Reading
140(1)
5 The Purified Quantum Theory
141(16)
5.1 Purification
142(1)
5.2 Isometric Evolution
143(11)
5.3 Coherent Quantum Instrument
154(1)
5.4 Coherent Measurement
155(1)
5.5 History and Further Reading
156(1)
Part III Unit Quantum Protocols
157(44)
6 Three Unit Quantum Protocols
159(22)
6.1 Non-local Unit Resources
160(2)
6.2 Protocols
162(9)
6.3 Optimality of the Three Unit Protocols
171(2)
6.4 Extensions for Quantum Shannon Theory
173(1)
6.5 Three Unit Qudit Protocols
174(6)
6.6 History and Further Reading
180(1)
7 Coherent Protocols
181(10)
7.1 Definition of Coherent Communication
182(2)
7.2 Implementations of a Coherent Bit Channel
184(1)
7.3 Coherent Dense Coding
185(2)
7.4 Coherent Teleportation
187(2)
7.5 The Coherent Communication Identity
189(1)
7.6 History and Further Reading
190(1)
8 The Unit Resource Capacity Region
191(10)
8.1 The Unit Resource Achievable Region
191(4)
8.2 The Direct Coding Theorem
195(1)
8.3 The Converse Theorem
196(4)
8.4 History and Further Reading
200(1)
Part IV Tools of Quantum Shannon Theory
201(214)
9 Distance Measures
203(29)
9.1 Trace Distance
204(8)
9.2 Fidelity
212(7)
9.3 Relationships between Trace Distance and Fidelity
219(4)
9.4 Gentle Measurement
223(3)
9.5 Fidelity of a Noisy Quantum Channel
226(4)
9.6 The Hilbert-Schmidt Distance Measure
230(1)
9.7 History and Further Reading
231(1)
10 Classical Information and Entropy
232(20)
10.1 Entropy of a Random Variable
233(4)
10.2 Conditional Entropy
237(2)
10.3 Joint Entropy
239(1)
10.4 Mutual Information
239(1)
10.5 Relative Entropy
240(1)
10.6 Conditional Mutual Information
241(2)
10.7 Information Inequalities
243(6)
10.8 Classical Information and Entropy of Quantum Systems
249(2)
10.9 History and Further Reading
251(1)
11 Quantum Information and Entropy
252(40)
11.1 Quantum Entropy
253(5)
11.2 Joint Quantum Entropy
258(3)
11.3 Potential yet Unsatisfactory Definitions of Conditional Quantum Entropy
261(2)
11.4 Conditional Quantum Entropy
263(2)
11.5 Coherent Information
265(2)
11.6 Quantum Mutual Information
267(3)
11.7 Conditional Quantum Mutual Information
270(2)
11.8 Quantum Relative Entropy
272(3)
11.9 Quantum Information Inequalities
275(15)
11.10 History and Further Reading
290(2)
12 The Information of Quantum Channels
292(35)
12.1 Mutual Information of a Classical Channel
293(6)
12.2 Private Information of a Wiretap Channel
299(4)
12.3 Holevo Information of a Quantum Channel
303(6)
12.4 Mutual Information of a Quantum Channel
309(5)
12.5 Coherent Information of a Quantum Channel
314(5)
12.6 Private Information of a Quantum Channel
319(6)
12.7 Summary
325(1)
12.8 History and Further Reading
326(1)
13 Classical Typicality
327(37)
13.1 An Example of Typicality
328(1)
13.2 Weak Typicality
329(2)
13.3 Properties of the Typical Set
331(2)
13.4 Application of Typical Sequences: Shannon Compression
333(2)
13.5 Weak Joint Typicality
335(3)
13.6 Weak Conditional Typicality
338(3)
13.7 Strong Typicality
341(9)
13.8 Strong Joint Typicality
350(2)
13.9 Strong Conditional Typicality
352(6)
13.10 Application: Shannon's Channel Capacity Theorem
358(4)
13.11 Concluding Remarks
362(1)
13.12 History and Further Reading
363(1)
14 Quantum Typicality
364(24)
14.1 The Typical Subspace
365(10)
14.2 Conditional Quantum Typicality
375(9)
14.3 The Method of Types for Quantum Systems
384(3)
14.4 Concluding Remarks
387(1)
14.5 History and Further Reading
387(1)
15 The Packing Lemma
388(13)
15.1 Introductory Example
389(1)
15.2 The Setting of the Packing Lemma
389(2)
15.3 Statement of the Packing Lemma
391(2)
15.4 Proof of the Packing Lemma
393(5)
15.5 Derandomization and Expurgation
398(2)
15.6 History and Further Reading
400(1)
16 The Covering Lemma
401(14)
16.1 Introductory Example
402(2)
16.2 Setting and Statement of the Covering Lemma
404(2)
16.3 Proof of the Covering Lemma
406(7)
16.4 History and Further Reading
413(2)
Part V Noiseless Quantum Shannon Theory
415(32)
17 Schumacher Compression
417(12)
17.1 The Information-Processing Task
418(2)
17.2 The Quantum Data-Compression Theorem
420(4)
17.3 Quantum Compression Example
424(1)
17.4 Variations on the Schumacher Theme
425(2)
17.5 Concluding Remarks
427(1)
17.6 History and Further Reading
427(2)
18 Entanglement Concentration
429(18)
18.1 An Example of Entanglement Concentration
430(3)
18.2 The Information-Processing Task
433(1)
18.3 The Entanglement Concentration Theorem
433(7)
18.4 Common Randomness Concentration
440(1)
18.5 Schumacher Compression versus Entanglement Concentration
441(4)
18.6 Concluding Remarks
445(1)
18.7 History and Further Reading
445(2)
Part VI Noisy Quantum Shannon Theory
447(179)
19 Classical Communication
451(26)
19.1 Naive Approach: Product Measurements at the Decoder
453(3)
19.2 The Information-Processing Task
456(2)
19.3 The Classical Capacity Theorem
458(5)
19.4 Examples of Channels
463(8)
19.5 Superadditivity of the Holevo Information
471(3)
19.6 Concluding Remarks
474(1)
19.7 History and Further Reading
475(2)
20 Entanglement-Assisted Classical Communication
477(31)
20.1 The Information-Processing Task
479(1)
20.2 A Preliminary Example
480(4)
20.3 The Entanglement-Assisted Classical Capacity Theorem
484(1)
20.4 The Direct Coding Theorem
484(9)
20.5 The Converse Theorem
493(8)
20.6 Examples of Channels
501(5)
20.7 Concluding Remarks
506(1)
20.8 History and Further Reading
507(1)
21 Coherent Communication with Noisy Resources
508(24)
21.1 Entanglement-Assisted Quantum Communication
509(5)
21.2 Quantum Communication
514(1)
21.3 Noisy Super-Dense Coding
515(3)
21.4 State Transfer
518(4)
21.5 Trade-off Coding
522(8)
21.6 Concluding Remarks
530(1)
21.7 History and Further Reading
531(1)
22 Private Classical Communication
532(18)
22.1 The Information-Processing Task
533(3)
22.2 The Private Classical Capacity Theorem
536(1)
22.3 The Direct Coding Theorem
536(9)
22.4 The Converse Theorem
545(1)
22.5 Discussion of Private Classical Capacity
546(3)
22.6 History and Further Reading
549(1)
23 Quantum Communication
550(35)
23.1 The Information-Processing Task
551(2)
23.2 The No-Cloning Theorem and Quantum Communication
553(1)
23.3 The Quantum Capacity Theorem
554(1)
23.4 The Direct Coding Theorem
555(7)
23.5 Converse Theorem
562(2)
23.6 An Interlude with Quantum Stabilizer Codes
564(7)
23.7 Example Channels
571(3)
23.8 Discussion of Quantum Capacity
574(5)
23.9 Entanglement Distillation
579(3)
23.10 History and Further Reading
582(3)
24 Trading Resources for Communication
585(33)
24.1 The Information-Processing Task
586(2)
24.2 The Quantum Dynamic Capacity Theorem
588(5)
24.3 The Direct Coding Theorem
593(3)
24.4 The Converse Theorem
596(10)
24.5 Examples of Channels
606(10)
24.6 History and Further Reading
616(2)
25 Summary and Outlook
618(8)
25.1 Unit Protocols
619(1)
25.2 Noiseless Quantum Shannon Theory
619(1)
25.3 Noisy Quantum Shannon Theory
620(3)
25.4 Protocols Not Covered in This Book
623(1)
25.5 Network Quantum Shannon Theory
624(1)
25.6 Future Directions
625(1)
Appendix A Miscellaneous Mathematics 626(7)
Appendix B Monotonicity of Quantum Relative Entropy 633(6)
References 639(14)
Index 653
Mark M. Wilde is an Assistant Professor with a joint appointment in the Department of Physics and Astronomy and the Center for Computation and Technology at Louisiana State University, Baton Rouge.
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