  Mixed states are introduced in physics in order to express our ignorance
about the actual state of a physical system and are represented in standard
quantum mechanics (QM) by density operators. Such operators also appear if one
considers a (pure) entangled state of a compound system $\Omega$ and performs
partial traces on the projection operator representing it. Yet, they do not
represent mixed states (or proper mixtures) of the subsystems in this case, but
improper mixtures, since the coefficients in the convex sums expressing them
never bear the ignorance interpretation. Hence, one cannot attribute states to
the subsystems of a compound physical system in QM (subentity problem). We
discuss here two alternative proposals that can be worked out within the
Brussels and Lecce approaches. We firstly summarize the general framework
provided by the former, which suggests that improper mixtures could be
considered as new pure states. Then, we show that improper mixtures can be
considered as true (yet nonpure) states also according to the latter. The two
proposals seem to be compatible notwithstanding their different terminologies.
