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Softcover ISBN:  9781470477776 
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Hardcover ISBN:  9781470475574 
Product Code:  GSM/243 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470477776 
Product Code:  GSM/243.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470477769 
Product Code:  GSM/243.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470477776 
eBook ISBN:  9781470477769 
Product Code:  GSM/243.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 243; 2024; 204 ppMSC: Primary 81; 68; 94; 20
This book presents the basics of quantum computing and quantum information theory. It emphasizes the mathematical aspects and the historical continuity of both algorithms and information theory when passing from classical to quantum settings.
The book begins with several classical algorithms relevant for quantum computing and of interest in their own right. The postulates of quantum mechanics are then presented as a generalization of classical probability. Complete, rigorous, and selfcontained treatments of the algorithms of Shor, Simon, and Grover are given. Passing to quantum information theory, the author presents it as a straightforward adaptation of Shannon's foundations to information theory. Both Shannon's theory and its adaptation to the quantum setting are explained in detail. The book concludes with a chapter on the use of representation theory in quantum information theory. It shows how all known entropy inequalities, including the celebrated strong subadditivity of von Neumann entropy, may be obtained from a representation theory perspective.
With many exercises in each chapter, the book is designed to be used as a textbook for a course in quantum computing and quantum information theory. Prerequisites are elementary undergraduate probability and undergraduate algebra, both linear and abstract. No prior knowledge of quantum mechanics or information theory is required.
ReadershipGraduate students and research mathematicians interested in the mathematical aspects of quantum computing.

Table of Contents

Classical and probabilistic computation

Quantum mechanics for quantum computation

Algorithms

Classical information theory

Language and background material for quantum information theory

Quantum information

Representation theory and quantum information

Algebra and linear algebra

Probability

Hints and answers to selected exercises

Bibliography

Index


Additional Material

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This book presents the basics of quantum computing and quantum information theory. It emphasizes the mathematical aspects and the historical continuity of both algorithms and information theory when passing from classical to quantum settings.
The book begins with several classical algorithms relevant for quantum computing and of interest in their own right. The postulates of quantum mechanics are then presented as a generalization of classical probability. Complete, rigorous, and selfcontained treatments of the algorithms of Shor, Simon, and Grover are given. Passing to quantum information theory, the author presents it as a straightforward adaptation of Shannon's foundations to information theory. Both Shannon's theory and its adaptation to the quantum setting are explained in detail. The book concludes with a chapter on the use of representation theory in quantum information theory. It shows how all known entropy inequalities, including the celebrated strong subadditivity of von Neumann entropy, may be obtained from a representation theory perspective.
With many exercises in each chapter, the book is designed to be used as a textbook for a course in quantum computing and quantum information theory. Prerequisites are elementary undergraduate probability and undergraduate algebra, both linear and abstract. No prior knowledge of quantum mechanics or information theory is required.
Graduate students and research mathematicians interested in the mathematical aspects of quantum computing.

Classical and probabilistic computation

Quantum mechanics for quantum computation

Algorithms

Classical information theory

Language and background material for quantum information theory

Quantum information

Representation theory and quantum information

Algebra and linear algebra

Probability

Hints and answers to selected exercises

Bibliography

Index