  We explore the synchronization phenomenon in the quantum few-body system of
spins with the non-local dissipation. Without the external driving, we find
that the system can exhibit stable oscillatory behaviors in the long-time
dynamics accompanied by the appearance of the purely imaginary eigenvalues of
the Liouvillian. Moreover, the oscillations of the next-nearest-neighboring
spins are completely synchronized revealed by the quantum trajectory analysis
within the stochastic Schr\"odinger equation. The possibility of the appearance
of the long-time oscillations in infinite-size lattice by means of cluster
mean-field approximation is also discussed.
