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Entanglement generation between distant nodes is a fundamental process in distributed quantum information processing. Qudits, high-dimensional quantum states, are promising candidates for enhancing entanglement distribution capabilities. However, the success probability of qudit entanglement distribution using Bell measurements is typically lower than that of conventional qubit-based protocols. In this paper, we propose an entanglement swapping protocol specifically designed for qutrits (three-dimensional quantum states). Our protocol employs photon-number encoding combined with an additional mode basis, such as polarization, effectively increasing the success probability. We show that the proposed qutrit protocol can achieve higher entanglement generation rates compared to conventional two-photon detection-based qubit protocols, especially under conditions of limited photon generation probability. Furthermore, we evaluate our protocol under realistic experimental imperfections, including photon loss and threshold detection, and show that it achieves high fidelity with probabilistic photon sources.
Tanji et al. (Mon,) studied this question.