We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schrödinger equation by using time-dependent Euler rotation together with a linear quench model to obtain the state of vacuum solution. Such state can be translated to the phase space picture to determine the Wigner distribution. We show that its Gaussian matrix 𝔾(t) can be used to directly cast the covariance matrix σ(t). To quantify the mixedness and entanglement of the state, one uses respectively linear and von Neumann entropies for three cases: fully symmetric, bi-symmetric and fully nonsymmetric. Then we determine the coherence, tripartite entanglement and local uncertainties and derive their dynamics. We show that the dynamics of all quantum information quantities are driven by the Ermakov modes. Finally, we use an homodyne detection to redistribute both resources of entanglement and coherence.

中文翻译：

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三个瞬态耦合谐振子中纠缠和相干的动力学和重新分布

我们研究了三个瞬态耦合谐振子中纠缠和相干的动力学和重新分布。我们通过使用时间相关的欧拉旋转和线性淬火模型来求解薛定谔方程，以获得真空解的状态。这种状态可以转换为相空间图以确定 Wigner 分布。我们证明了它的高斯矩阵𝔾(吨)可用于直接转换协方差矩阵σ(吨). 为了量化状态的混合性和纠缠，我们分别使用线性熵和冯诺依曼熵来表示三种情况：完全对称、双对称和完全非对称。然后我们确定相干性、三方纠缠和局部不确定性并推导出它们的动力学。我们表明，所有量子信息量的动力学都是由 Ermakov 模式驱动的。最后，我们使用零差检测来重新分配纠缠和相干资源。