Real-field Hong–Ou–Mandel interference of indistinguishable coherent photons via long optical injection-locking over 50 km fiber

Measurement-device-independent quantum key distribution (MDI-QKD) has garnered significant attention for enabling security-loophole-free quantum communication. Successful MDI-QKD protocols rely on performing a two-photon Bell-state measurement at an intermediate node, where achieving a high-visibility Hong-Ou-Mandel (HOM) interference pattern between two independent coherent photons is crucial. In this study, we present an approach for developing indistinguishable coherent photon sources over 50 km of optical fiber under real-world conditions. We introduce the long optical injection-locking (long-OIL) technique, which enables frequency locking between two long-distance coherent photons separated by distances exceeding the coherence length of the master laser. Utilizing the long-OIL technique, we achieved time-resolved HOM interference with a visibility of 48(2)%, which is close to the theoretical limits of 50% for two independent continuous-wave coherent photons. Our results indicate that the long-OIL platform is a promising solution for MDI-QKD with repeaterless secret-key capacity.