Essay on the foundations of classical and quantum information theories.

Abstract

This work is an essay that assesses some important tools in Classical and Quantum information theory. The concept of qubit (quantum two level systems) is introduced in a simple manner by using a few statistical optics concepts (Stokes vectors and coherence matrices). Unlike most texts of Quantum information in which the qubits of spin are often addressed, in this text the concept of polarization qubit is developed. Shannon and Von Neumann entropy functions are introduced formally and, therefore, some of the particularities of classical and quantum information theory are highlighted and confronted The most important properties of these entropies are demonstrated with detail. The concept of majorization is introduced for both cases: the quantum and theclassical ones. The Jaynes problem is discussed in the light of classical theory of information (The Jaynes principle), in the quantum case, this problem-which is still open- is approached in a simple and intuitive manner.