The combination of the polarization and spatial photonic degrees of freedom open interesting possibilities in the quantum optics and quantum-information domains. The ability to produce and transform beams carrying orbital angular momentum – the optical vortices - has allowed the development of important techniques with potential applications to quantum information. In this seminar I will present some optical devices to quantum information and I will talk about the topological phase, associated with the double connectedness of the SO  representation in terms of maximally entangled states. Under local unitary operations on their polarization and transverse degrees of freedom, the vector vortices can only acquire discrete geometric phase values, 0 or π, associated with closed paths belonging to different homotopy classes on the SO(3) manifold. As the meaning results I will show that the topological phase can be evidenced through interferometric measurements and that a quantitative relationship between the concurrence and the fringes visibility can be derived as well.
 C. E. R. Souza, J. A. O. Huguenin and A. Z. Khoury Topological phase structure of vector vortex beams, JOSA-A 31, No. 5 1007 (2014).
 C. E. R. Souza, J. A. O. Huguenin, P. Milman and A. Z. Khoury Topological Phase for Spin-Orbit Transformations on a Laser Beam PRL 99, 160401 (2007).
 C. E. R. Souza and A. Z. Khoury A Michelson controlled-not gate with a single-lens astigmatic mode converter Optics Express 18, No. 9 9207 (2010).