Quantum Information Theory and Quantum Statistics

Quantum Information Theory and Quantum Statistics

von: Dénes Petz

Springer-Verlag, 2007

ISBN: 9783540746362 , 216 Seiten

Format: PDF

Kopierschutz: Wasserzeichen

Windows PC,Mac OSX Apple iPad, Android Tablet PC's

Preis: 60,98 EUR

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Mehr zum Inhalt

Quantum Information Theory and Quantum Statistics


 

Preface

6

Contents

8

Introduction

11

Prerequisites from Quantum Mechanics

13

2.1 Postulates of Quantum Mechanics

14

2.2 State Transformations

24

2.3 Notes

32

2.4 Exercises

32

Information and its Measures

35

3.1 Shannon’s Approach

36

3.2 Classical Source Coding

38

3.3 von Neumann Entropy

44

3.4 Quantum Relative Entropy

47

3.5 R ´ enyi Entropy

55

3.6 Notes

59

3.7 Exercises

60

Entanglement

62

4.1 Bipartite Systems

62

4.2 Dense Coding and Teleportation

72

4.3 Entanglement Measures

76

4.4 Notes

78

4.5 Exercises

79

More About Information Quantities

81

5.1 Shannon’s Mutual Information

81

5.2 Markov Chains

82

5.3 Entropy of Partied Systems

84

5.4 Strong Subadditivity of the von Neumann Entropy

86

5.5 The Holevo Quantity

87

5.6 The Entropy Exchange

88

5.7 Notes

89

5.8 Exercises

90

Quantum Compression

91

6.1 Distances Between States

91

6.2 Reliable Compression

93

6.3 Universality

96

6.4 Notes

98

6.5 Exercises

98

Channels and Their Capacity

99

7.1 Information Channels

99

7.2 The Shannon Capacity

100

7.3 Holevo Capacity

103

7.4 Classical-quantum Channels

112

7.5 Entanglement-assisted Capacity

113

7.6 Notes

114

7.7 Exercises

114

Hypothesis Testing

116

8.1 The Quantum Stein Lemma

117

8.2 The Quantum Chernoff Bound

123

8.3 Notes

126

8.4 Exercises

127

Coarse-grainings

128

9.1 Basic Examples

128

9.2 Conditional Expectations

130

9.3 Commuting Squares

138

9.4 Superadditivity

140

9.5 Sufficiency

140

9.6 Markov States

145

9.7 Notes

148

9.8 Exercises

149

State Estimation

150

10.1 Estimation Schemas

150

10.2 Cram ´ er–Rao Inequalities

157

10.3 Quantum Fisher Information

161

10.4 Contrast Functionals

169

10.5 Notes

170

10.6 Exercises

171

Appendix: Auxiliary Linear and Convex Analysis

172

11.1 Hilbert Spaces and Their Operators

172

11.2 Positive Operators and Matrices

174

11.3 Functional Calculus for Matrices

177

11.4 Distances

182

11.5 Majorization

184

11.6 Operator Monotone Functions

187

11.7 Positive Mappings

196

11.8 Matrix Algebras

202

11.9 Conjugate Convex Function

205

11.10 Some Trace Inequalities

206

11.11 Notes

207

11.12 Exercises

207

Bibliography

211

Index

216