Overview
- Presents a general and rigorous framework of quantum information based on von Neumann algebras
- Makes a comprehensive study of different types of quantum divergences
- Updates Petz' previous work on reversibility/sufficiency for quantum operations
Part of the book series: Mathematical Physics Studies (MPST)
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Table of contents (8 chapters)
Keywords
About this book
In the first half of this monograph, the different types of quantum f-divergences and the Rényi-type divergences mentioned above in the general von Neumann algebra setting are presented for study. While quantum information has been developing mostly in the finite-dimensional setting, it is widely believed that von Neumann algebras provide the most suitable framework in studying quantum information and related subjects. Thus, the advance of quantum divergences in von Neumann algebras will be beneficial for further development of quantum information.
Quantum divergences are functions of two states (or more generally, two positive linear functionals) on a quantum system and measure the difference between the two states. They are often utilized to address such problems as state discrimination, error correction, and reversibility of quantum operations. In the second half of the monograph, the reversibility/sufficiency theory for quantum operations (quantum channels) between von Neumann algebras via quantum f-divergences is explained, thus extending and strengthening Petz' previous work.
For the convenience of the reader, an appendix including concise accounts of von Neumann algebras is provided.
Reviews
“The contents of the book presents very interesting topics for quantum information scientists … . I would like to recommend this book for two kinds of special groups of scientists: pure mathematicians, who want to learn the power of quantum computing, and quantum information theorists, who are tired of quantum computing. … this book will be a good guide. For the second group, including people like me, this book stimulates the dormant instincts about quantum information theory.” (Kabgyun Jeong, zbMATH 1476.81004, 2022)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Quantum f-Divergences in von Neumann Algebras
Book Subtitle: Reversibility of Quantum Operations
Authors: Fumio Hiai
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-981-33-4199-9
Publisher: Springer Singapore
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021
Hardcover ISBN: 978-981-33-4198-2Published: 27 January 2021
Softcover ISBN: 978-981-33-4201-9Published: 27 January 2022
eBook ISBN: 978-981-33-4199-9Published: 26 January 2021
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: X, 194
Number of Illustrations: 139 b/w illustrations
Topics: Mathematical Physics, Quantum Physics, Operator Theory, Functional Analysis