Probing Higher Dimensions of Hilbert Space in Experiment

Using the correlated pairs produced in spontaneous parametric down-conversion, one can extract quantum states effectively defined in a Hilbert space of any dimension N. Furthermore, using just beam splitters and phase shifters one can build any unitary operator in the laboratory. We briefly discuss how this can be done, what kind of states could easily be produced in the laboratory, and we will discuss one explicit result pertaining to photon bunching in an N-dimensional Hilbert space.