Quantum Systems, Channels, Information
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Alexander S. Holevo
About this book
The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world.
The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.
Author / Editor information
Alexander S. Holevo, Steklov Mathematical Institute, Moscow, Russia.
Reviews
"Written in a mathematically rigorous way, the book gives an accessible and self-contained introduction to quantum theory of information and presents fundamental results in the subject." Mathematical Reviews
"The book is suited for researchers, and lecturers who find the respective matter worked out and well ordered, as well as for students who may check their grasp, since any step is accompanied by task-oriented exercises. […] This book mediates the origins and the development up to the present state of art in a very instructive manner. It can be best recommended." Zentralblatt für Mathematik
Supplementary Materials
Topics
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Frontmatter
i -
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Preface
v -
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Contents
ix - Part I. Basic structures
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Chapter 1. Vectors and operators
3 -
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Chapter 2. States, observables, statistics
10 -
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Chapter 3. Composite systems and entanglement
34 - Part II. The primary coding theorems
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Chapter 4. Classical entropy and information
57 -
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Chapter 5. The classical-quantum channel
74 - Part III. Channels and entropies
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Chapter 6. Quantum evolutions and channels
103 -
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Chapter 7. Quantum entropy and information quantities
132 - Part IV. Basic channel capacities
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Chapter 8. The classical capacity of quantum channel
155 -
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Chapter 9. Entanglement-assisted classical communication
180 -
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Chapter 10. Transmission of quantum information
195 - Part V. Infinite systems
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Chapter 11. Channels with constrained inputs
243 -
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Chapter 12. Gaussian systems
266 -
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Bibliography
333 -
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Index
346