Theoretical and Mathematical Physics

By: DÃ©nes Petz

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Hardcover | 12 November 2007

At a Glance

Hardcover
228 Pages

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23.5 x 15.24 x 1.91

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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, a field to which the author has contributed significantly himself, it emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader for deeper studies, not the least through a selection of well chosen exercises.

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"This book covers a great deal of central topics and actual problems of quantum information theory except quantum computation and cryptography. It is an introduction which emphasizes the mathematical interesting and beauty aspects of quantum and information theory as well as their synthesis on an ambitious level suitable for graduate students. It is offering mathematically rigorous and elegant proofs for central propositions and with this respect it can serve teachers and researchers doing their work." (K.-E. Hellwig, Zentralblatt MATH, Vol. 1145, 2008)

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You Can Find This Book In

Non-Fiction Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Engineering & Technology Technology in General Instruments & Instrumentation Engineering Mathematics Probability & Statistics Computing & I.T.Computer Science Mathematical Theory of Computation

Introduction	p. 1
Prerequisites from Quantum Mechanics	p. 3
Postulates of Quantum Mechanics	p. 4
State Transformations	p. 14
Notes	p. 22
Exercises	p. 22
Information and its Measures	p. 25
Shannon's Approach	p. 26
Classical Source Coding	p. 28
von Neumann Entropy	p. 34
Quantum Relative Entropy	p. 37
Renyi Entropy	p. 45
Notes	p. 49
Exercises	p. 50
Entanglement	p. 53
Bipartite Systems	p. 53
Dense Coding and Teleportation	p. 63
Entanglement Measures	p. 67
Notes	p. 69
Exercises	p. 70
More About Information Quantities	p. 73
Shannon's Mutual Information	p. 73
Markov Chains	p. 74
Entropy of Partied Systems	p. 76
Strong Subadditivity of the von Neumann Entropy	p. 78
The Holevo Quantity	p. 79
The Entropy Exchange	p. 80
Notes	p. 81
Exercises	p. 82
Quantum Compression	p. 83
Distances Between States	p. 83
Reliable Compression	p. 85
Universality	p. 88
Notes	p. 90
Exercises	p. 90
Channels and Their Capacity	p. 91
Information Channels	p. 91
The Shannon Capacity	p. 92
Holevo Capacity	p. 95
Classical-quantum Channels	p. 104
Entanglement-assisted Capacity	p. 105
Notes	p. 106
Exercises	p. 106
Hypothesis Testing	p. 109
The Quantum Stein Lemma	p. 110
The Quantum Chernoff Bound	p. 116
Notes	p. 119
Exercises	p. 120
Coarse-grainings	p. 121
Basic Examples	p. 121
Conditional Expectations	p. 123
Commuting Squares	p. 131
Superadditivity	p. 133
Sufficiency	p. 133
Markov States	p. 138
Notes	p. 141
Exercises	p. 142
State Estimation	p. 143
Estimation Schemas	p. 143
Cramer-Rao Inequalities	p. 150
Quantum Fisher Information	p. 154
Contrast Functionals	p. 162
Notes	p. 163
Exercises	p. 164
Appendix: Auxiliary Linear and Convex Analysis	p. 165
Hilbert Spaces and Their Operators	p. 165
Positive Operators and Matrices	p. 167
Functional Calculus for Matrices	p. 170
Distances	p. 175
Majorization	p. 177
Operator Monotone Functions	p. 180
Positive Mappings	p. 189
Matrix Algebras	p. 195
Conjugate Convex Function	p. 198
Some Trace Inequalities	p. 199
Notes	p. 200
Exercises	p. 200
Bibliography	p. 205
Index	p. 211
Table of Contents provided by Ingram. All Rights Reserved.

Theoretical and Mathematical Physics

At a Glance

Hardcover

Industry Reviews

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