Using Polarization to Control the Phase of Spatial Modes for Application in Quantum Information

Exploiting spatial modes and polarization, we experimentally demonstrate the realization of a conditional pi-phase shift. Our approach is based on an optical circuit where the polarization and transverse degrees of freedom control the Gouy phase which is applied on Hermite-Gaussian beams. Our results show good agreement with the simulation of the optical circuit. As an application, we propose the implementation of a two-qubit quantum phase gate, where the qubits are encoded on the Hermite-Gaussian modes and linear polarization states.