This book originated in a course given first to computer scientists at the University of Nice–Sophia Antipolis in October 2003, and later to second-year graduate students at the same University.

Quantum information is a field which at present is undergoing intensive development and, owing to the novelty of the concepts involved, it seems to me it should be of interest to a broad range of scientists beyond those actually working in the field. My goal here is to give an elementary introduction which is accessible not only to physicists, but also to mathematicians and computer scientists desiring an initiation into the subject. This initiation includes the essential ideas from quantum mechanics, and the only prerequisite is knowledge of linear algebra at the undergraduate level and some physics background at the high school level (except in Chapter 6 where I discuss the physical implementations of quantum computers and more physics background is required). In order to make it easier for mathematicians and computer scientists to follow, I give an elementary presentation of the Dirac notation. Quantum physics is an extremely large subject, and so I have attempted to limit the introductory concepts to the barest minimum needed to understand quantum information.

In Chapter 2, I introduce the concept of the quantum bit or qubit using the simplest possible example, that of the photon polarization. This example allows me to present the essential ideas of quantum mechanics and explain quantum cryptography. Chapter 3 generalizes the concept of qubit to other physical systems like spin 1/2 and the two-level atom, and explains how qubits can be manipulated by means of Rabi oscillations.