Visualizing and witnessing first-order coherence, Bell nonlocality and purity by using a quantum steering ellipsoid in the non-inertial frame

A quantum steering ellipsoid (QSE) is a visual characterization for bipartite qubit systems, and it is also a novel avenue for describing and detecting quantum correlations. Herein, by using a QSE, we visualize and witness the first-order coherence (FOC), Bell nonlocality (BN) and purity under non-inertial frames. Also, the collective influences of the depolarizing channel and the non-coherence-generating channel (NCGC) on the FOC, BN and purity are investigated in the QSE formalism. The results reveal that the distance from the center of the QSE to the center of the Bloch sphere visualizes the FOC of a bipartite system, the lengths of the QSE semiaxis visualize the BN, and the QSE's shape and position dominate the purity of the system. One can capture the FOC, BN and purity via the shape and position of the QSE in the non-inertial frame. The depolarizing channel (the NCGC) gives rise to the shrinking and degradation (the periodical oscillation) of the QSE. One can use these traits to visually characterize and detect the FOC, BN and purity under the influence of external noise. Of particular note is that the condition for the QSE to achieve the center of the Bloch sphere cannot be influenced by the depolarizing channel and the NCGC. The characterization shows that the conditions for the disappearance of the FOC are invariant under the additional influences of the depolarizing channel and NCGC.