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 [Formula: see text] can be used to directly cast the covariance matrix [Formula: see text]. 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.
In this work, we investigate the Schrödinger dynamics of photon excitation numbers and entanglement in a system composed by two non-resonant time-dependent coupled oscillators. By considering π periodically pumped parameters (oscillator frequencies and coupling) and using suitable transformations, we show that the quantum dynamics can be determined by two classical Meissner oscillators. We then study analytically the stability of these differential equations and the dynamics of photon excitations and entanglement in the quantum system numerically. Our analysis shows two interesting results, which can be summarized as follows: (i) Classical instability of classical analog of quantum oscillators and photon excitation numbers (expectations Nj) are strongly correlated, and (ii) photon excitations and entanglement are connected to each other. These results can be used to shed light on the link between quantum systems and their classical counterparts and provide a nice complement to the existing works studying the dynamics of coupled quantum oscillators.
The Milburn dynamics of three non resonant ultra-strongly coupled oscillators are resolved by using symplectic geometry. The Milburn dynamics of virtual excitations and how they affect the pairwise entanglement are looked at. It is found that the dynamics of excitations and entanglement experience similar profiles against time, physical parameters, and decoherence rate. Furthermore, it is shown that the extinction of excitations entails separability, which demonstrates the hierarchy between entanglement and virtual excitations. Additionally, the effects of physical parameters on the redistribution of virtual excitations among the three bi-partitions are analyzed. As a result, the violation of the monogamy of excitations is shown as in quantum discord. This implies that excitations can be considered as signatures of quantum correlations beyond entanglement. Besides, it is emphasized that the treatment can be used to model coupled quantum circuits in real situations (with decoherence).
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