Information, Entropy and Time in Quantum Systems

Information theory has been crucial to develop modern digital communications. As quantum computing is evolving and getting increasing attention, the development of communication between quantum devices appears as a natural consequence. Researchers around the world have defined quantum versions of classical information theory concepts and explored their differences. Not only the community has foundnew version of the classical concepts, but has also defined many new concept that arise from the laws of quantum mechanics--- and so have no classical analogous. In this work, we present two main topics: a study of the evolution of quantum entropies during a decoherence process and the analysis of entanglement fidelity for different quantum channels acting on one qubit messages,both in a general case and a concrete example. We show how relaxing the Markovianity assumption on the evolution of a system complicates the study of long time bounds of its von Neumann entropy. We report unsuccessful attempts in generalizing existing results on such quantity to quantum Rênyi and Tsallis entropies--- in this case assuming Markovian evolution described by Lindblad master equation. Finally, we compute the Entanglement fidelity for Random Pauli-X, Dephasing, Depolarizing, Werner-Holevo, Generalized Pauli andAmplitude damping channels. The quantity is computed first for a general density matrix and then for a particular two letter message. This computation allows to find guidelines on how to choose the optimal letters or channel in a real case scenario.