'An extraordinary book on the deep principles behind quantum theory.' Nicolas Gisin, Universite de Geneve 'Part quantum mechanics textbook, part original research contribution, this book is a fascinating, audacious effort to 'rebuild quantum mechanics from the ground up', presenting it as the logical consequence of simple information-theoretic postulates. Students wishing to learn quantum information should read it and do all the exercises!' Scott Aaronson, Massachusetts Institute of Technology 'From the earliest days of quantum theory to the present, physicists have been pleased with the excellent results it yields but also unsettled (in varying degrees) by the fact that its mathematical forms do not always have clear physical interpretations. Some efforts to resolve this problem in recent decades have focused on replacing mathematical postulates with informational postulates. The authors take this approach here ... [intended for] not just physicists but also mathematicians and computer scientists. The first section, about one-third of the book's length, is flagged by the authors as suitable for an undergraduate course and might well serve so at the highest undergraduate levels ... The two remaining sections are aimed at a master's-level audience; the final section lays out the derivation of quantum theory from six informational principles ... A generous number (more than 200) practice exercises are included, with solutions available for selected problems.' K. D. Fisher, Choice