Controlled generation of maximally entangled qudits using twin photons

We show theoretically how two-photon fields generated by spontaneous parametric down-conversion can be used for creating maximally entangled states of multidimensional quantum systems, qudits. Logical states are defined by using different transverse spatial modes of the twin photons. These spatial modes are created by sending the components of the two-photon field through an array of multislits. The present experimental facilities allow generating maximally entangled states up to an eight-dimensional system.