Entanglement-based clock syntonization for quantum key distribution networks. Demonstration over a 50 km-long link

We present the implementation of a time synchronization protocol as part of an experimentally deployed entanglement-based quantum key distribution (QKD) link. The system is deployed over 48 km of optical fibers across the M\'etropole C\^ote d'Azur and enables secret cryptographic key exchange between two remote users, with an average rate of 7 kbps. We exploit the time correlation of paired photons generated by a high-quality source of energy-time entanglement implemented in the QKD link to synchronize two rubidium clocks located at the end stations. The level of stability achieved guarantees a time offset between the clocks under 12 ps at all time. We also show that this protocol requires less hardware than a typical synchronization protocol for QKD that would distribute a reference clock signal between the users.