Entanglement generation between remote qubit systems is the central tasks for quantum communication. Future quantum networks will have to be compatible with low-loss telecom bands and operate with large separation between qubit nodes. Single-click heralding schemes can be used to increase entanglement rates at the cost of needing an optically phase-synchronized architecture. In this paper we present such a phase synchronization scheme for a metropolitan quantum network, operating in the low-loss telecom L band. To overcome various challenges such as communication delays and optical power limitations, the scheme consists of multiple tasks that are individually stabilized. We characterize each task, identify the main noise sources, motivate the design choices, and describe the synchronization schemes. The performance of each of the tasks is quantified by a transfer-function measurement that investigates the frequency response and feedback bandwidth. Finally we investigate the resulting optical phase stability of the fully deployed system over a continuous period of 10 h, reporting a short-term stability standard deviation of 𝜎 ≈30∘ and a long-term stability of the average optical phase to within a few degrees. The scheme presented served as a key enabling technology for a nitrogen-vacancy-center-based metropolitan quantum link. This scheme is of interest for other quantum network platforms that benefit from an extendable and telecom-compatible phase-synchronization solution.@en

We present stability criteria for equilibria of a class of linear complementarity systems, subjected to discrete and distributed delay. We present necessary and
sufficient conditions for local exponential stability, inferred from the spectrum location of a corresponding system of delay differential algebraic equations. Subsequently, we obtain sufficient LMI-based conditions for global asymptotic
stability using Lyapunov–Krasovskii functionals.@en