What is it about?
This book constitutes an elementary introduction to rings and fields, especially 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.
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Why is it important?
The existing literature on rings and fields is primarily mathematical. There are a great deal 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. The present 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.
Perspectives
This book 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, computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may be also of interest to undergraduate students in mathematics.
Maurice Kibler
Institut de Physique Nucléaire de Lyon (CNRS/IN2P3 and Université Claude Bernard Lyon 1)
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This page is a summary of: Galois Fields, January 2017, Elsevier,
DOI: 10.1016/b978-1-78548-235-9.50002-6.
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