Quantum information theory 1st Edition by Mark Wilde ISBN 1107034256 978-1107034259
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ISBN 10: 1107034256
ISBN 13: 978-1107034259
Author: Mark M. Wilde
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
Table of contents:
Part I Introduction
1Concepts in Quantum Shannon Theory
1.1 Overview of the Quantum Theory
1.2 The Emergence of Quantum Shannon Theory
2 Classical Shannon Theory
2.1 Data Compression
2.2 Channel Capacity
2.3 Summary
Part II The Quantum Theory
3 The Noiseless Quantum Theory
3.1 Overview
3.2 Quantum Bits
3.3 Reversible Evolution
3.4 Measurement
3.5 Composite Quantum Systems
3.6 Summary and Extensions to Qudit States
3.7 History and Further Reading
4 The Noisy Quantum Theory
4.1 Noisy Quantum States
4.2 Measurement in the Noisy Quantum Theory
4.3 Composite Noisy Quantum Systems
4.4 Noisy Evolution
4.5 Summary
4.6 History and Further Reading
5 The Purified Quantum Theory
5.1 Purification
5.2 Isometric Evolution
5.3 Coherent Quantum Instrument
5.4 Coherent Measurement
5.5 History and Further Reading
Part III Unit Quantum Protocols
6 Three Unit Quantum Protocols
6.1 Non-local Unit Resources
6.2 Protocols
6.3 Optimality of the Three Unit Protocols
6.4 Extensions for Quantum Shannon Theory
6.5 Three Unit Qudit Protocols
6.6 History and Further Reading
7 Coherent Protocols
7.1 Definition of Coherent Communication
7.2 Implementations of a Coherent Bit Channel
7.3 Coherent Dense Coding
7.4 Coherent Teleportation
7.5 The Coherent Communication Identity
7.6 History and Further Reading
8 The Unit Resource Capacity Region
8.1 The Unit Resource Achievable Region
8.2 The Direct Coding Theorem
8.3 The Converse Theorem
8.4 History and Further Reading
Part IV Tools of Quantum Shannon Theory
9 Distance Measures
9.1 Trace Distance
9.2 Fidelity
9.3 Relationships between Trace Distance and Fidelity
9.4 Gentle Measurement
9.5 Fidelity of a Noisy Quantum Channel
9.6 The Hilbert-Schmidt Distance Measure
9.7 History and Further Reading
10 Classical Information and Entropy
10.1 Entropy of a Random Variable
10.2 Conditional Entropy
10.3 Joint Entropy
10.4 Mutual Information
10.5 Relative Entropy
10.6 Conditional Mutual Information
10.7 Information Inequalities
10.8 Classical Information and Entropy of Quantum Systems
10.9 History and Further Reading
11 Quantum Information and Entropy
11.1 Quantum Entropy
11.2 Joint Quantum Entropy
11.3 Potential yet Unsatisfactory Definitions of Conditional Quantum Entropy
11.4 Conditional Quantum Entropy
11.5 Coherent Information
11.6 Quantum Mutual Information
11.7 Conditional Quantum Mutual Information
11.8 Quantum Relative Entropy
11.9 Quantum Information Inequalities
11.10 History and Further Reading
12 The Information of Quantum Channels
12.1 Mutual Information of a Classical Channel
12.2 Private Information of a Wiretap Channel
12.3 Holevo Information of a Quantum Channel
12.4 Mutual Information of a Quantum Channel
12.5 Coherent Information of a Quantum Channel
12.6 Private Information of a Quantum Channel
12.7 Summary
12.8 History and Further Reading
13 Classical Typicality
13.1 An Example of Typicality
13.2 Weak Typicality
13.3 Properties of the Typical Set
13.4 Application of Typical Sequences: Shannon Compression
13.5 Weak Joint Typicality
13.6 Weak Conditional Typicality
13.7 Strong Typicality
13.8 Strong Joint Typicality
13.9 Strong Conditional Typicality
13.10 Application: Shannon’s Channel Capacity Theorem
13.11 Concluding Remarks
13.12 History and Further Reading
14 Quantum Typicality
14.1 The Typical Subspace
14.2 Conditional Quantum Typicality
14.3 The Method of Types for Quantum Systems
14.4 Concluding Remarks
14.5 History and Further Reading
15 The Packing Lemma
15.1 Introductory Example
15.2 The Setting of the Packing Lemma
15.3 Statement of the Packing Lemma
15.4 Proof of the Packing Lemma
15.5 Derandomization and Expurgation
15.6 History and Further Reading
16 The Covering Lemma
16.1 Introductory Example
16.2 Setting and Statement of the Covering Lemma
16.3 Proof of the Covering Lemma
16.4 History and Further Reading
Part V Noiseless Quantum Shannon Theory
17 Schumacher Compression
17.1 The Information-Processing Task
17.2 The Quantum Data-Compression Theorem
17.3 Quantum Compression Example
17.4 Variations on the Schumacher Theme
17.5 Concluding Remarks
17.6 History and Further Reading
18 Entanglement Concentration
18.1 An Example of Entanglement Concentration
18.2 The Information-Processing Task
18.3 The Entanglement Concentration Theorem
18.4 Common Randomness Concentration
18.5 Schumacher Compression versus Entanglement Concentration
18.6 Concluding Remarks
18.7 History and Further Reading
Part VI
Noisy Quantum Shannon Theory
19 Classical Communication
19.1 Naive Approach: Product Measurements at the Decoder
19.2 The Information-Processing Task
19.3 The Classical Capacity Theorem
19.4 Examples of Channels
19.5 Superadditivity of the Holevo Information
19.6 Concluding Remarks
19.7 History and Further Reading
20 Entanglement-Assisted Classical Communication
20.1 The Information-Processing Task
20.2 A Preliminary Example
20.3 The Entanglement-Assisted Classical Capacity Theorem
20.4 The Direct Coding Theorem
20.5 The Converse Theorem
20.6 Examples of Channels
20.7 Concluding Remarks
20.8 History and Further Reading
21Coherent Communication with Noisy Resources
21.1 Entanglement-Assisted Quantum Communication
21.2 Quantum Communication
21.3 Noisy Super-Dense Coding
21.4 State Transfer
21.5 Trade-off Coding
21.6 Concluding Remarks
21.7 History and Further Reading
22 Private Classical Communication
22.1 The Information-Processing Task
22.2 The Private Classical Capacity Theorem
22.3 The Direct Coding Theorem
22.4 The Converse Theorem
22.5 Discussion of Private Classical Capacity
22.6 History and Further Reading
23 Quantum Communication
23.1 The Information-Processing Task
23.2 The No-Cloning Theorem and Quantum Communication
23.3 The Quantum Capacity Theorem
23.4 The Direct Coding Theorem
23.5 Converse Theorem
23.6 An Interlude with Quantum Stabilizer Codes
23.7 Example Channels
23.8 Discussion of Quantum Capacity
23.9 Entanglement Distillation
23.10 History and Further Reading
24 Trading Resources for Communication
24.1 The Information-Processing Task
24.2 The Quantum Dynamic Capacity Theorem
24.3 The Direct Coding Theorem
24.4 The Converse Theorem
24.5 Examples of Channels
24.6 History and Further Reading
25 Summary and Outlook
25.1 Unit Protocols
25.2 Noiseless Quantum Shannon Theory
25.3 Noisy Quantum Shannon Theory
25.4 Protocols Not Covered in This Book
25.5 Network Quantum Shannon Theory
25.6 Future Directions
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