  The effect of a local trace-preserving single-qubit channel on a two-qubit
state is investigated in the picture of the quantum steering ellipsoids (QSE).
The phenomenon of locally increased quantum correlation is visualized in this
picture. We strictly prove that a $B$-side two-qubit discordant state can be
locally prepared from a classical state by a trace-preserving channel on qubit
$B$ if and only if its QSE of $B$ is a non-radial line segment. For states with
higer-dimensional QSEs, the phenomenon of locally increased quantum correlation
generally happens when the shape of the QSE is like a baguette. Based on this
observation, we find a class of entangled states whose quantum discord can be
increased by the local amplitude damping channel. Further, We find that the
local quantum channel does not increase the size of QSEs of either qubit $A$ or
qubit $B$, for the needle-shape QSE states, as well as the Bell diagonal states
with higher-dimensional QSE.
