odeword is allowed one out of two pos- sible states, and this corresponds to the most fundamental representation of classical information. In quantum information theory (QIT), and its derivative, quantum computation (QC), the elementary unit of information is the quantum bit or qubit. As we shall see, the striking property of the qubit is to escape any definition of being 0 or 1. It is correct, however, to say that it can be either 0 or 1. To clarify, somewhat, such a mystery, consider a closed box with a coin inside. We shake the box. The coin must then be resting in the heads or tails position (excluding here any other possibility, for simplicity). The question is, "What is the coin's position?" The intuitive and classical answer is, "It must be either heads or tails." According to the quantum definition, the coin is described by a qubit. The answer is that the coin position, or state, is "neither heads nor tails, but a superposition of both." As long as we do not open the box, we cannot know in which state the coin actually exists. By opening the box, we make a measurement of the coin state, and the outcome is a classical bit of information, namely heads or tails. This basic example provides an intuitive notion of the nature of the qubit, which I shall formalize through this chapter. In the above, we have used different new terms, such as state, superposition of states, and measurement, which (to some readers) represents as many hints of the domain of quantum mechanics. In this introductory chapter, we shall approach the notion of qubit without approaching quantum mechanics any closer. Indeed, there is no need to present a more complicated picture if we can introduce the qubit and its properties and formalism by simpler means. We have realized from the preceding explanation that the qubit is a piece of information that combines in some ways the information of both 0 and 1. Therefore, we may simply view the qubit as a two-dimensional (2D) vector, with one dimension defining the 0 information component, and the 