  Any two-qubit state can be represented, geometrically, as an ellipsoid with a
certain size and a center located within the Bloch sphere of one of the qubits.
Points of this ellipsoid represent the post-measurement states when the other
qubit is measured. Based on the most demolition concept in the definition of
quantum discord, we study the amount of demolition when the two
post-measurement states, represented as two points on the steering ellipsoid,
have the most distinguishability. We use trace distance as a measure of
distinguishability and obtain the maximum distinguishability for some classes
of states, analytically. Using the optimum measurement that gives the most
distinguishable steered states, we extract quantum correlation of the state and
compare the result with the quantum discord. It is shown that there are some
important classes of states for which the most demolition happens exactly at
the most distinguished steered points. Correlations gathered from the most
distinguished post-measurement states provide a faithful and tight upper bound
touching the quantum discord in most of the cases.
