Dynamics and Redistribution of Entanglement and Coherence in Three Time-Dependent Coupled Harmonic Oscillators

We study the dynamics and redistribution of entanglement and coherence in three time-dependent coupled harmonic oscillators. We resolve the Schr\"{o}dinger 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 $\mathbb{G}(t)$ can be used to directly cast the covariance matrix $\sigma(t)$. 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 non symmetric. 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.