  We discuss the appearance of fractional topological phases on cyclic
evolutions of entangled qudits encoded on photonic degrees of freedom. We show
how the spatial correlations between photons generated by spontaneous
parametric down conversion can be used to evidence the multiple topological
phases acquired by entangled qudits and the role played by the Hilbert space
dimension. A realistic experimental proposal is presented with numerical
predictions of the expected results.
