Quantum information theory and quantum statistics
It has been a long way since C. E. Shannon started to explore the mathematical background of communcation and information theory [Bell Syst. Tech. J. 27, 379-423, 623-656 (1948; Zbl 1154.94303)]. Today, the vast development in understanding quantum phenomena offers impressive new perspectives and applications, many of them surveyed Dénes Petz's “Quantum information theory and quantum statistics” [Theoretical and Mathematical Physics. Berlin: Springer (2008; Zbl 1145.81002)].
As reviewer K.-E. Hellwig puts it,“This book covers a great deal of central topics and actual problems of quantum information theory except quantum computation and cryptography. It is an introduction which emphasizes the mathematical interesting and beauty aspects of quantum and information theory as well as their synthesis on an ambitious level suitable for graduate students. It is offering mathematically rigorous and elegant proofs for central propositions and with this respect it can serve teachers and researchers doing their work.”