This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics.
The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access.
This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering).
Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics.
- Contains numerous examples that accompany the text
- Includes an important chapter on mutually unbiased bases
- Helps physicists and theoretical chemists understand this area of mathematics
Masters and PhD students and researchers in the field of physics, quantum physics and quantum information theory
1. The Structures of Ring and Field
2. Galois Fields
3. Galois Rings
4. Mutually Unbiased Bases
5. Appendix on Number Theory and Group Theory
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- © ISTE Press - Elsevier 2018
- 12th September 2017
- ISTE Press - Elsevier
- eBook ISBN:
- Hardcover ISBN:
Maurice Kibler is Professor Emeritus at Claude Bernard University Lyon 1 in France. His research concerns the role of symmetries in the elaboration of models in various domains of physics (sub-atomic, atomic, molecular and condensed matter physics). He is also interested in quantum information.
Claude Bernard University Lyon 1, France
"There are a great number of books in the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. The goal of this book is to give an accessible introduction with lots of examples to the topic for non-mathematicians." -Zentralblatt MATH