Witnessing quantum steering and nonlocal advantage of quantum coherence via quantum steering ellipsoid

Abstract An arbitrary bipartite state can be visually characterized through a quantum steering ellipsoid (QSE), and different nonclassical correlations can be visually revealed via the geometric traits of the QSE. Here, we characterize the QSE of bipartite Bell diagonal states subject to the influences of the bit flip (BF), the depolarizing (DP), and the phase damping (PD) channels, and ascertain the influences of various noise channels on the QSE. By employing nonlinear asymmetric quantum steering criterion (NAC), linear asymmetric quantum steering criterion (LAC), quantum steering criterion from the entropic uncertainty relation (SCEUR), and the shape of the QSE, we reveal and witness the quantum steering and the nonlocal advantage of quantum coherence (NAQC) of the system under these noise channels. It turns out that noise channels can significantly affect the shape of the QSE, one can effectively capture quantum steering and the NAQC via the QSE. Among the NAC, LAC, and SCEUR, the LAC (the NAC) is the most promising avenue for detecting the quantum steering under the DP and PD channels (under the the BF channels). It is particularly important to note that the shape of the QSE can visually display the abilities of these criteria in witnessing quantum steering. Moreover, based on the ${l_1}$ norm of coherence, the NAQC can be achieved under the BF, DP, and PD channels if the sum of three semiaxis lengths of the QSE can surpass $\sqrt 6 $.