  We employ a quantum trajectory approach to characterize synchronization and
phase-locking between open quantum systems in nonequilibrium steady states. We
exemplify our proposal for the paradigmatic case of two quantum Van der Pol
oscillators interacting through dissipative coupling. We show the deep impact
of synchronization on the statistics of phase-locking indicators and other
correlation measures defined for single trajectories, spotting a link between
the presence of synchronization and the emergence of large tails in the
probability distribution for the entanglement along trajectories. Our results
shed new light on fundamental issues regarding quantum synchronization
providing new methods for its precise quantification.
