Quantum Synchronization and Entanglement Generation.

We study synchronization in a two-node network built out of the smallest possible self-sustained oscillator: a spin-1 oscillator. We first demonstrate that phase locking between the quantum oscillators can be achieved, even for limit cycles that cannot be synchronized to an external semiclassical signal. Building upon the analytical description of the system, we then clarify the relation between quantum synchronization and the generation of entanglement. These findings establish the spin-based architecture as a promising platform for understanding synchronization in complex quantum networks.