Criterion of quantum phase synchronization in continuous variable systems by local measurement Phase synchronization was proved to be unbounded in quantum level, but the witness of phase synchronization is always expensive in terms of the quantum resource and nonlocal measurements involved. Based on the quantum uncertainty relation, we construct two local criterions for the phase synchronization in this paper. The local criterions indicate that the phase synchronization in the quantum level can be witnessed only by the local measurements, and the deduction has been verified in the optomechanics system in numerical way. Besides, by analyzing the physical essence of the phase synchronization in quantum level, we show that one can prepare a state, which describes two synchronized oscillators with no entanglement between them. Thus, the entanglement resource is not necessary in the occurrence of the ideal phase synchronization, and also the reason for this phenomenon is discussed.

Multipartite Entanglement Generation in a Structured Environment In this paper, we investigate the entanglement generation of nqubit states in a model consisting of n independent qubits, each coupled to a harmonic oscillator which is in turn coupled to a bath of N additional harmonic oscillators with nearestneighbor coupling. With analysis, we can find that the steady multipartite entanglement with different values can be generated after a longtime evolution for different sizes of the quantum system. Under weak coupling between the system and the harmonic oscillator, multipartite entanglement can monotonically increase from zero to a stable value. Under strong coupling, multipartite entanglement generation shows a speedup increase accompanied by some oscillations as nonMarkovian behavior. Our results imply that the strong coupling between the harmonic oscillator and the N additional harmonic oscillators, and the large size of the additional oscillators will enhance nonMarkovian dynamics and make it take a very long time for the entanglement to reach a stable value. Meanwhile, the couplings between the additional harmonic oscillators and the decay rate of additional harmonic oscillators have almost no effect on the multipartite entanglement generation. Finally, the entanglement generation of the additional harmonic oscillators is also discussed.