Estudo de estados de variáveis contínuas Gaussianos e não-Gaussianos monomodais sob efeito de um canal dissipativo

Abstract

The objective of this thesis is to study continuous variables states, single mode Gaussian and non-Gaussian, evolving under the effect of a dissipative channel. Thereby, we define two problems: study the quantum properties of the state and the dissipative channel. To address these problems, we review briefly the mathematical tools that we used, namely: quantum estimation theory, master equations and continuous variables. In the following chapters we study, respectively: (i) the problem of estimation of the loss parameter, i.e. the dissipation parameter, ofa bosonic channel using non-Gaussian states; (ii) how some quantum properties of single mode Gaussian states and coherent superposition states evolve under a non-unitary dynamics. Some results for the first item, we estimate, in an optimal way, the loss parameter of the channel, for example using Fock states; for the second item we provide the characteristic times and the initial condition limits of the state in order that they show, effectively, the squeezing property. We show also a comparison between the evolution of the von Neumann entropy of a single mode Gaussian state under the influence of a reservoir with infinite degrees of freedom and one with only few degrees of freedom (but some of them showing instability). Moreover we present preliminary results and perspectives, among them a work where we are studying how a single mode Gaussian state, evolving unitarily accordingto a Hamiltonian containing characteristic of instability and non-unitarilyas a master equation, and what is the relation that exist between dissipation and instability.