Gaussian states in continuous variable quantum information

ISBN 88-7088-483-X (Bibliopolis, Napoli, 2005) http://www.bibliopolis.it These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A special emphasis has been given to the phase space analysis of quantum dynamics and to the role of Gaussian states in continuous variable quantum information. We thank Giuseppe Marmo for his invitation to write these lecture notes and for his kind assistance in the various stages of this project. MGAP would like to thank Mauro D’Ariano for the exciting introduction he gave me to this fields, and Rodolfo Bonifacio, who gave me the possibility of establishing a research group at the University of Milano. MGAP also thanks Maria Bondani and Alberto Porzio for the continuing discussions on quantum optics over these years. Many colleagues contributed in several ways to the materials in this volume. In particular we thank Alessio Serafini, Nicola Piovella, Mary Cola, Andrea Rossi, Fabrizio Illuminati, Konrad Banaszek, Salvatore Solimeno, Virginia D’Auria, Silvio De Siena, Alessandra Andreoni, Alessia Allevi, Emiliano Puddu, Antonino Chiummo, Paolo Perinotti, Lorenzo Maccone, Paolo Lo Presti, Massimiliano Sacchi, Jarda Řeháček, Berge Englert, Paolo Tombesi, David Vitali, Stefano Mancini, Geza Giedke, Jaromir Fiurášek and Valentina De Renzi. A special thank to Alessio Serafini for his careful reading and comments on various portions of the manuscript. One of us (SO) would like to remember here a friend, Mario Porta: my work during these years is also due to your example in front of the difficulties of life.