Abstract
M.A. Lohe first proposed the high-dimensional Kuramoto model with symmetry-breaking terms (Quantum synchronization over quantum networks, Journal of Physics A: Mathematical and Theoretical, 43:465301, 2010), which is the real form of a quantum network synchronization model. For the homogeneous case, by analyzing the limit set and the spectrum of the linearized model, the almost global synchronization is derived from the topology of some kind of connecting graphs.