Petz Quantum Information Theory and Quantum Statistics

1. Auflage 2007
ISBN: 978-3-540-74636-2
Verlag: Springer Berlin Heidelberg
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 216 Seiten

Reihe: Theoretical and Mathematical Physics

This concise and readable book addresses primarily readers with a background in classical statistical physics and introduces quantum mechanical notions as required. Conceived as a primer to bridge the gap between statistical physics and quantum information, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not least through a selection of well chosen exercises.

Autoren/Hrsg.

Petz, Dénes

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Introduction;11
4;Prerequisites from Quantum Mechanics;13
4.1;2.1 Postulates of Quantum Mechanics;14
4.2;2.2 State Transformations;24
4.3;2.3 Notes;32
4.4;2.4 Exercises;32
5;Information and its Measures;35
5.1;3.1 Shannon’s Approach;36
5.2;3.2 Classical Source Coding;38
5.3;3.3 von Neumann Entropy;44
5.4;3.4 Quantum Relative Entropy;47
5.5;3.5 R ´ enyi Entropy;55
5.6;3.6 Notes;59
5.7;3.7 Exercises;60
6;Entanglement;62
6.1;4.1 Bipartite Systems;62
6.2;4.2 Dense Coding and Teleportation;72
6.3;4.3 Entanglement Measures;76
6.4;4.4 Notes;78
6.5;4.5 Exercises;79
7;More About Information Quantities;81
7.1;5.1 Shannon’s Mutual Information;81
7.2;5.2 Markov Chains;82
7.3;5.3 Entropy of Partied Systems;84
7.4;5.4 Strong Subadditivity of the von Neumann Entropy;86
7.5;5.5 The Holevo Quantity;87
7.6;5.6 The Entropy Exchange;88
7.7;5.7 Notes;89
7.8;5.8 Exercises;90
8;Quantum Compression;91
8.1;6.1 Distances Between States;91
8.2;6.2 Reliable Compression;93
8.3;6.3 Universality;96
8.4;6.4 Notes;98
8.5;6.5 Exercises;98
9;Channels and Their Capacity;99
9.1;7.1 Information Channels;99
9.2;7.2 The Shannon Capacity;100
9.3;7.3 Holevo Capacity;103
9.4;7.4 Classical-quantum Channels;112
9.5;7.5 Entanglement-assisted Capacity;113
9.6;7.6 Notes;114
9.7;7.7 Exercises;114
10;Hypothesis Testing;116
10.1;8.1 The Quantum Stein Lemma;117
10.2;8.2 The Quantum Chernoff Bound;123
10.3;8.3 Notes;126
10.4;8.4 Exercises;127
11;Coarse-grainings;128
11.1;9.1 Basic Examples;128
11.2;9.2 Conditional Expectations;130
11.3;9.3 Commuting Squares;138
11.4;9.4 Superadditivity;140
11.5;9.5 Sufficiency;140
11.6;9.6 Markov States;145
11.7;9.7 Notes;148
11.8;9.8 Exercises;149
12;State Estimation;150
12.1;10.1 Estimation Schemas;150
12.2;10.2 Cram ´ er–Rao Inequalities;157
12.3;10.3 Quantum Fisher Information;161
12.4;10.4 Contrast Functionals;169
12.5;10.5 Notes;170
12.6;10.6 Exercises;171
13;Appendix: Auxiliary Linear and Convex Analysis;172
13.1;11.1 Hilbert Spaces and Their Operators;172
13.2;11.2 Positive Operators and Matrices;174
13.3;11.3 Functional Calculus for Matrices;177
13.4;11.4 Distances;182
13.5;11.5 Majorization;184
13.6;11.6 Operator Monotone Functions;187
13.7;11.7 Positive Mappings;196
13.8;11.8 Matrix Algebras;202
13.9;11.9 Conjugate Convex Function;205
13.10;11.10 Some Trace Inequalities;206
13.11;11.11 Notes;207
13.12;11.12 Exercises;207
14;Bibliography;211
15;Index;216