Invariant of quantum correlation in qubit-qutrit systems under local de-phasing

In this research work, we investigate the dynamics of quantum correlation and entanglement via direct measure and negativity for a class of mixed qubit-qutrit states assuming that only the qutrit is under the action of a de-phasing channel. We demonstrate for a separable state, the quantum correlation is invariant under the action of de-phasing channel. Also, we saw that even though the entanglement in the qubit-qutrit state disappears in a finite time interval, the partial coherent left in the system enables quantum correlation to remain invariant throughout the time evolution.