A Group Theoretic Approach to Quantum Information / by Masahito Hayashi.
Hayashi, Masahito. author.
2017
QC173.96-174.52
Available Online

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Title A Group Theoretic Approach to Quantum Information / by Masahito Hayashi.
Author Hayashi, Masahito. author.
ISBN 9783319452418
331945241X
9783319452395
3319452398
DOI https://doi.org/10.1007/978-3-319-45241-8
Published Cham : Springer International Publishing : Imprint: Springer, 2017.
Language English
Description 1 online resource.
Item Number 10.1007/978-3-319-45241-8 doi
Call Number QC173.96-174.52
Dewey Decimal Classification 530.12
Summary This textbook is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory.
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Digital File Characteristics text file PDF
Available in Other Form Print version: 9783319452395
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All Resources
Foundation of Quantum Theory
Quantum Channel, Information Quantities, and Their Mathematical Structure
Quantum Entanglement and Its Quantification
Group Covariance and Optimal Information Processing
Quantum Error Correcting Code and Its Application
Universal Information Processings.

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