Geometric quantum discords under Hierarchical-environment with filtering operator

Abstract

We study the dynamic creation of two different geometric quantum discords (GQDs) defined, respectively, via the Hilbert-Schmidt norm (GQD-2) and trace norm (GQD-1) between the two qubits, which are prepared initially in a zero discord two-qubit X -shape state, and subject to a two layers environment that consists of a lossy cavity coupled to the W -coupled lossy cavities. We find that the GQD-2 and GQD-1 exhibit oscillatory behavior in the regime of the strong coupling between the qubit and firstlayer cavity environment. And in both the weak and strong coupling regimes, for the greater the number of cavities in the second-layer environment, the GQDs reach their peak value in a larger time and go to zero more slowly. But in the qubit-cavity coupling, the coupling between two nearest neighbor cavities and the decay rate of cavities in the second-layer environment have the opposite effect on the GQDs. Furthermore, the maximum value of GQDs remains unchanged and the steady value increases, or they both decrease, depending on the threshold value of coupling between the two layers environment. Finally, we propose an effective strategy to improve the GQD-2 and GQD-1 by using local filtering operation.