Optimal Entanglement Concentration For Photonic Qutrits Encoded In Path Variables

We report on a technique that allows for the entanglement manipulation of qudit states encoded in the linear transverse momentum of photon pairs generated in the process of spontaneous parametric downconversion. It relies on the use of spatial light modulators and interferometric techniques for implementing the desired local measurements. As an application of our method we perform the optimal entanglement concentration of entangled qutrit states, where maximally entangled states are obtained with the maximal success probability. The procedure of entanglement concentration is fundamental for many quantum information tasks, thus showing the potential of our technique for future experimental investigations considering high-dimensional Hilbert spaces.