Exploring maximal steered coherence and entanglement via quantum steering ellipsoid framework

All two-qubit states can be characterized visually by a quantum steering ellipsoid (QSE) inside the Bloch sphere, and their quantum resources (such as entanglement and discord) can be directly reflected via the geometric properties of QSE. In this work, we obtain QSE of bipartite Werner state interacting with a reservoir and probe the effects of the strong coupling regime and weak coupling regime on the maximal steered coherence (MSC) and concurrence in QSE framework. It is concluded that the MSC can be identified by the length of x or y semiaxis of ellipsoid. Meanwhile, the concurrence is related to the lengths of x and z semiaxes of QSE. The information can flow bidirectionally between the qubit system and the non-Markovian environment, which can induce the shrink, inflation and movement of ellipsoid in the Bloch sphere. On the contrary, due to the decoherence of information within Markovian environment, the QSE gradually shrinks and then eventually disappears in the north pole of Bloch sphere. Therefore, the evolutions of MSC and concurrence can be mapped by the aforementioned dynamics of QSE. The results also reveal that MSC and concurrence can be enhanced by suppressing the degradation of ellipsoid’s semiaxis. Moreover, we investigate the inflation of QSE under filtering operation and derive the condition of increasing MSC. An optimal operation strength of filtering operation is also obtained. It is worth noting that MSC and concurrence can be frozen by the optimal strength in the strong coupling and weak coupling regimes.