This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.
Maria Luisa Dalla Chiara, professor emeritus of Logic and Philosophy of Science at the University Florence is a past president of the "International Quantum Structures Association", of the "Italian Society of Logic and Philosophy of Science" and a past vice-president of the "Division of Logic, Methodology and Philosophy of Science". She is the author of books and articles concerning the following fields: quantum logic, quantum computation, foundations and philosophy of quantum theory, semantics of physical theories, theories of meaning, semantics of music.
Roberto Giuntini, professor of Logic and Philosophy of Science at the University of Cagliari, is president of the "Italian Society of Logic and Philosophy of Science" and past president of the "International Quantum Structures Association". His research centers around the logico-algebraic structures of quantum theory and quantum computation. In 1998 he was awarded the Birkhoff-von Neumann Prize.
Roberto Leporini received an MSc degree cum laude in Computer Science in 1999 and a PhD in Computer Science in 2004, both from the University of Milan. Since 2005 he is an assistant professor at the University of Bergamo. His main research interests are: quantum computing, quantum optics, quantum computational structures and logic. He has published over 40 papers in international journals and holds a patent on the construction of quantum circuits. He is the president of the "International Quantum Structures Association".
Giuseppe Sergioli received an MSc degree in Theoretical Physics at the University of Catania and a PhD in Logic and Philosophy of Science at the University of Cagliari, where he is now an assistant professor. His main research interests are: quantum computing, quantum computational structures and quantum computational logics. He is the author of several papers published in prominent journals in the areas of physics, logic, foundations of physics and computer science.
