Fig. 3: Quantum interference and quantum state tomography for 4- and 8-level entangled qudits.

a, b Measured two-photon quantum interferences of 4-level entangled qudits over the H22-H30 and H20-H32 channels, respectively. Extracted raw visibilities of 90.14% ± 1.08% (a) and 89.45% ± 1.14% (b) exceeded the threshold necessary to violate Bell’s inequality for 4 levels (i.e., 81.70%). The gray markers correspond to accidental coincidences, which were used to evaluate the visibilities without background noise. c Density matrix ρ retrieved from quantum state tomography measurements performed in a system-tailored set of projections (see Methods), from which we extracted a fidelity of 84.44% ± 1.03% and an entanglement of formation equal to  1.992. d Measured joint temporal distribution showing correlations between the eight different time bins. e, f Measured two-photon quantum interferences of 8-level entangled qudits over the H22-H30 and H20-H32 channels, respectively. Extracted raw visibilities were 91.23% ± 1.04% (e) and 90.76% ± 1.01% (f), both exceeding the threshold necessary to violate Bell’s inequality for 8 levels (i.e., 89.56%). The gray markers correspond to accidental coincidences, which were used to evaluate the visibilities without background noise. Error bars are estimated using Poisson statistics.