Experimental robustness of the fractional topological phase to dephasing noise

We observe experimentally the fractional topological phase (FTP) robustness to the dephasing noise in two-qudit photonic systems. We use a source of photon pairs generated by spontaneous parametric down-conversion, hyperentangled in the polarization and photon path degrees of freedom. The dephasing noise is described theoretically via Kraus maps and experimentally implemented via the spatial light modulator. The FTP is a great candidate to explore in the implementation of quantum processing and communication due to its robustness to dephasing noise.

Figure 1

Experimental setup (top view) for measuring the FTP in a two-qudit photonic system under dephasing noise: HWP, half waveplate; QWP, quarter waveplate; $L_p, L_C, L_i$, and $L_f$: lenses; D, dichroic mirror; MS, multiple slits; SLM, spatial light modulator; PBS, polarizing beam splitter; D1 and D2, avalanche photon detectors.

Figure 2

Interference patterns in the two-photon coincidence counts $C$ for two ququarts. The solid lines are the fitting curves according to Eq. (6). Black squares correspond to $t=0$, red circles to $t=0.5$, and blue triangles to $t=1$. The noise level is (a) 0%, (b) 50%, (c) 75%, and (d) 100%.

Figure 3

Normalized experimental visibilities as a function of the noise level: (a) visibility when the $\mathrm{SU}\left(d\right)$ evolution starts and (b) visibility at the end of the $\mathrm{SU}\left(d\right)$ evolution. The experimental points for qudits with $d=2$ (red squares), $d=3$ (black circles), and $d=4$ (blue triangles) are plotted along with the theoretical curves [31] (solid lines).

Figure 4

Interference patterns in the two-photon coincidence counts $C$ for two qubits. The solid lines are the fitting curves according to Eq. (6). Black squares correspond to $t=0$, red circles to $t=0.5$, and blue triangles to $t=1$. The noise level is (a) 0%, (b) 50%, (c) 75%, and (d) 100%.

Figure 5

Interference patterns in the two-photon coincidence counts $C$ for two qutrits. The solid lines are the fitting curves according to Eq. (6). Black squares correspond to $t=0$, red circles to $t=0.5$, and blue triangles to $t=1$. The noise level is (a) 0%, (b) 50%, (c) 75%, and (d) 100%.