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* [3] 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.

[1] 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).

[2] 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).

[3] 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).