Robustness of the fractional topological phase to dephasing

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In this work, we demonstrate theoretically via Kraus maps that the fractional topological phase in qudits is robust to phase noise. In our proposal, dephasing noise is inserted in an optical setup designed for measuring the fractional topological phase on photonic qudits encoded in path variables after local unitary operations are applied. Qudit states can be prepared with photon pairs generated by spontaneous parametric down-conversion crossing a multiple-slit array. Polarization as an additional degree of freedom and a two-photon longitudinal interferometer are the basic ingredients of the proposed setup. Although the visibility of the interference pattern decreases when noise is added, our calculation shows that the topological phase is preserved. This result stimulates further studies for the use of fractional topological phase in quantum gates due to its robustness in environments where phase noise is present.