  We investigate quantum synchronization phenomenon within the complex network
constituted by coupled optomechanical systems and prove the unknown identical
quantum states can be shared or distributed in the quantum network even though
the topology is varying. Considering a channel constructed by quantum
correlation, we show that quantum synchronization can sustain and maintain high
levels in Markovian dissipation for a long time. We analyze state sharing
process between two typical complex networks, that is, a small-world network
corresponding to linear motif state sharing and a scale-free network
corresponding to whole network sharing, respectively. Our results predict that
linked nodes can be directly synchronized in small-world network, but the whole
network will be synchronized only if some specific synchronization conditions
are satisfied. Furthermore, we give the synchronization conditions analytically
through analyzing network dynamics. This proposal paves the way for studying
multi-interaction synchronization and achieving an effective quantum
information processing in complex network.
