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Quantum information theory and quantum statistics

Author: Dénes Petz
Publisher: Berlin : Springer, ©2008.
Series: Theoretical and mathematical physics (Springer (Firm))
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"Based on lectures given by the author, this book focuses on providing reliable introductory explanations of key concepts of quantum information theory and quantum statistics - rather than on results. The mathematically rigorous presentation is supported by numerous examples and exercises and by an appendix summarizing the relevant aspects of linear analysis. Assuming that the reader is familiar with the content of  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Dénes Petz
ISBN: 9783540746348 354074634X 9783540746362 3540746366
OCLC Number: 191865087
Description: ix, 214 pages : illustrations ; 24 cm.
Contents: 1. Introduction --
2. Prerequisites from Quantum Mechanics --
2.1. Postulates of Quantum Mechanics --
2.2. State Transformations --
2.3. Notes --
2.4. Exercises --
3. Information and its Measures --
3.1. Shannon's Approach --
3.2. Classical Source Coding --
3.3. von Neumann Entropy --
3.4. Quantum Relative Entropy --
3.5. Renyi Entropy --
3.6. Notes --
3.7. Exercises --
4. Entanglement --
4.1. Bipartite Systems --
4.2. Dense Coding and Teleportation --
4.3. Entanglement Measures --
4.4. Notes --
4.5. Exercises --
5. More About Information Quantities --
5.1. Shannon's Mutual Information --
5.2. Markov Chains --
5.3. Entropy of Partied Systems --
5.4. Strong Subadditivity of the von Neumann Entropy --
5.5. The Holevo Quantity --
5.6. The Entropy Exchange --
5.7. Notes --
5.8. Exercises --
6. Quantum Compression --
6.1. Distances Between States --
6.2. Reliable Compression --
6.3. Universality --
6.4. Notes --
6.5. Exercises --
7. Channels and Their Capacity --
7.1. Information Channels --
7.2. The Shannon Capacity --
7.3. Holevo Capacity --
7.4. Classical-quantum Channels --
7.5. Entanglement-assisted Capacity --
7.6. Notes --
7.7. Exercises --
8. Hypothesis Testing --
8.1. The Quantum Stein Lemma --
8.2. The Quantum Chernoff Bound --
8.3. Notes --
8.4. Exercises --
9. Coarse-grainings --
9.1. Basic Examples --
9.2. Conditional Expectations --
9.3. Commuting Squares --
9.4. Superadditivity --
9.5. Sufficiency --
9.6. Markov States --
9.7. Notes --
9.8. Exercises --
10. State Estimation --
10.1. Estimation Schemas --
10.2. Cramer-Rao Inequalities --
10.3. Quantum Fisher Information --
10.4. Contrast Functionals --
10.5. Notes --
10.6. Exercises --
11. Appendix: Auxiliary Linear and Convex Analysis --
11.1. Hilbert Spaces and Their Operators --
11.2. Positive Operators and Matrices --
11.3. Functional Calculus for Matrices --
11.4. Distances --
11.5. Majorization --
11.6. Operator Monotone Functions --
11.7. Positive Mappings --
11.8. Matrix Algebras. 11.9. Conjugate Convex Function --
11.10. Some Trace Inequalities --
11.11. Notes --
11.12. Exercises.
Series Title: Theoretical and mathematical physics (Springer (Firm))
Responsibility: Dénes Petz.
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Abstract:

Conceived as a primer to bridge the gap between statistical physics and quantum information, this title emphasizes concepts and thorough discussions of the fundamental notions and prepares the reader  Read more...

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From the reviews: "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 Read more...

 
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