Emaranhamento em caminhadas quânticas

Abstract

In this work, we study the quantum walks analyzing their main properties. First, we revise the notion of classical random walks, on which the quantum walks are based. Thus, we present two models of discrete-time quantum walks, the coined and scattering quantum walks, and then the equivalence between them. From mapping one model onto the other, we obtain an energy-dependent coined quantum walk. Then, we introduce the two most explored properties in the literature for these systems, entanglement and standard deviation. After that, we include inhomogeneity in the spatial degree of freedom, firstly based on works already developed for the coined quantum walks and extending the analysis for the scattering quantum walks considering point interactions as scattering centers that vary with the position on the network. In all the cases considered, we analyze the entanglement and standard deviation. For example, for the standard deviation, we notice that by increasing the inhomogeneity, the dispersion decreases compared to the homogeneous case. Still, it keeps being larger than the random walk, featuring a superdiffusive behavior in most cases. Similarly, the entanglement goes losing stability and presents oscillation without approaches a limit value as the inhomogeneity is introduced in the networks.