Fig. 1: Simplified schematic of the star-topology quantum network.

The user node, relay node and the central node are implemented on a single silicon photonic chip. A trigger signal from the pulsed laser source is employed for the synchronization of the TCSPC (1) at the relay node and another trigger signal from the pulse laser is encoded on an optical carrier and sent to the central node for synchronization with the TCSPC (2) at the central node. An optical delay line is used between the user node and the relay node in order to temporally match the arrival time of the idler photons from the user node and the relay node. The visibility of the Hong-Ou-Mandel interference between two thermal fields is used as an error signal for the delay adjustment. The heralding signal in the user node is encoded on an optical carrier and employed in the active stabilization system of the two-photon interference. In the relay node, the signal and idler photons from one output port of the VBS-UMZI are used for synchronization of the user node and the relay node. In this schematic, the blue and green solid lines are the optical and electronic paths in the setup, respectively. (BSM Bell state measurement, BS beam splitter, VBS-UMZI variable beam splitter unbalanced Mach-Zehnder interferometer, \({\chi }^{(3)}\) third-order nonlinear source, TCSPC time-correlated single-photon counter, Sync synchronization signal, DL delay line)