Long-time protection of correlations and coherence in squeezed thermal bath

We investigate the dynamics of correlations in terms of quantum discord, dissonance, entanglement and classical correlation for a system formed by two qubits in a dephasing model. Each qubit is embedded in a squeezed thermal bath evolving independently and initially in a state with maximally mixed marginals via a nondemolition interaction. We reveal how the correlations may be protected during the evolution in weak and strong coupling regimes for various ranges of the temperature. We show the existence of a sudden conversion between the quantum discord and classical correlation occurring at a critical time. By appropriately choosing the model parameters, long-time protection of the quantum discord can be correspondingly achieved without any perturbation from the decoherence effect. On the other hand, the quantum dissonance can be used to foretell the behaviour of the correlations during the evolution. Moreover, we examine the time dependence of the coherence and squeezing entropy for the qubits.