The book is the result of 20 years of teaching and research by the three authors in the fields of quantum foundations and quantum information, which culminated in two long joint papers [Phys. Rev. A 81 062348 (2010) and 84 012311 (2011)] that derive quantum theory from six simple information-theoretical principles. We have now the opportunity of presenting quantum theory in a radically new way, based on a conceptual understanding from the new principles. By “quantum theory” we mean the general theory of physical systems that lies at the core of “quantum mechanics,” the latter broadly viewed as the quantum generalization of classical Hamiltonian mechanics. The book will not cover applications to “mechanics,” but rather focus on applications to quantum information. For this reason, and with the aim of keeping the center of attention more on conceptual issues, rather than on the mathematical technicalities, we consider finite numbers of finite-dimensional systems, and restrict to probabilities of finite set of events, with some extensions to the infinite/continuous case discussed in the notes at the end of chapters.

The book includes 220 exercises and problems. The exercises are given within the body of each chapter, and selected solutions can be found at the end of that chapter. The exercises represent an integral part of the book and we warmly recommend the reader to solve them (or to check out the solutions), because the results proven therein are often used in our arguments. The problems presented at the end of each chapter build up additional knowledge and problem-solving skills, not strictly needed for the understanding of the arguments, but it is still recommended to solve them (or study the solutions). References, historical comments, and citations are provided in the notes at the end of chapters.

The book can be used for teaching at all levels, ranging from undergraduate, to master, up to PhD, and for pursuing personal research interests.