  We examine, in correlated mixed states of qudit-qubit systems, the set of all
conditional qubit states that can be reached after local measurements at the
qudit based on rank-1 projectors. While for a similar measurement at the qubit,
the conditional post-measurement qudit states lie on the surface of an
ellipsoid, for a measurement at the qudit we show that the set of
post-measurement qubit states can form more complex solid regions. In
particular, we show the emergence, for some classes of mixed states, of sets
which are the convex hull of solid ellipsoids and which may lead to cone-like
and triangle-like shapes in limit cases. We also analyze the associated
measurement dependent conditional entropy, providing a full analytic
determination of its minimum and of the minimizing local measurement at the
qudit for the previous states. Separable rank-2 mixtures are also discussed.
