Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book develops theoretical methods in the area of quantum technologies, namely, quantum teleportation, quantum channel capacities, quantum estimation, and quantum key distribution. It focuses on the graduate students approaching the study of quantum continuous variables, or for researchers keen on gaining a first grounding in the theoretical methods to describe such systems, be it from the angle of quantum optics, of controlled quantum dynamics or, more widely, of quantum technologies. The book introduces the instruments to deal with the Hilbert space description of Gaussian systems, and analyses their quantum correlations, their information and communication capacity, their application to quantum metrology, and their use in quantum key distribution. It reports some slightly more specific notions concerning the singular value decomposition and Schur complements.