Fractional topological phase on spatially encoded photonic qudits

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.