  Manipulation of qudits in optical tables is a difficult and nonscalable task.
The use of integrated optical circuits opens new possibilities for the
generation, manipulation, and characterization of high dimensional states
besides the ease of transmission of these states through an optical fiber. In
this work we propose photonic circuits to perform minimum quantum state
tomography of path qudits and show how to determine all the constituents
parameters of these circuits (beam splitters and phase shifters). Our
strategies were based on the symmetries of the involved POVMs (positive
operator-valued measures) suggested for minimum tomography and allowed us to
obtain interferometers smaller than those obtained by other already known
methods. The calculations of the transmittances and reflectivities of the beam
splitters were made using the definition of probability operators in extended
Hilbert spaces and the application of Naimark's theorem. The employment of
equidistant states for the definition of the POVM elements allowed us to
develop a recipe applicable to the tomography of qudits of any dimension,
generalizing our scheme.
