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

Abstract

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 the QSE, we visualize and witness the first-order coherence (FOC), the Bell nonlocality (BN), and the purity under the non-inertial frames. Also, the collective influences of the depolarizing channel and the non-coherence-generating channel (NCGC) on the FOC, the BN, and the purity are investigated in the QSE formalism. The results reveal that the distance from the center of QSE to the center of the Bloch sphere visualizes the FOC of bipartite system, the lengths of QSE semiaxis visualize the BN, and the QSE’s shape and position dominant the purity of system. One can capture the FOC, the BN, and the purity via the shape and position of the QSE in the non-inertial frames. The depolarizing channel (The NCGC) gives rise to the shrinking and degrading (the periodical oscillation) of the QSE. One can use these traits to visually characterize and detect the FOC, the BN, and the purity under the influences of external noises. Of particular note is that the condition for the QSE achieving the Bloch sphere’s center cannot be influenced by the depolarizing channel and the NCGC. The characteristics visualize that the conditions of the FOC disappearance are invariant under the additional influences of depolarizing channel and the NCGC, respectively.