Quantum clock synchronization with the silicon-chip based entangled photon source

Leveraging the properties of quantum entanglement and squeezing, quantum clock synchronization offers significant advantages in improving precision and security. For scalable quantum clock synchronization networks, developing an accurate time deviation analysis model is essential to characterize long-term timing stability and enable reliable deployment in real-world systems. This paper proposes a synchronization stability analysis model that establishes the theoretically achievable time deviation based on the Cramér-Rao lower bound. We experimentally validate this model using a round-trip quantum clock synchronization protocol over 50 km of fiber, employing an integrated silicon-photonic chip that generates frequency-entangled photon pairs via four-wave mixing. Results show a synchronization accuracy of 15.08 ps and a time deviation of 901 fs at an averaging time of 10,240 seconds, while our model analysis shows a standard deviation of 12.21 ps. This work provides a fundamental framework for building robust, large-scale quantum networks.