Preparation and characterization of arbitrary states of four-dimensional qudits based on biphotons

We report interferometric schemes to prepare arbitrary states of four-dimensional qudits (ququarts) based on biphoton states of ultrafast-pumped frequency-nondegenerate spontaneous parametric down-conversion. Preparation and tomographic characterization of a few examples of general single-ququart states, a pure state, a completely mixed state, and a partially-mixed state, are experimentally demonstrated.