On the Physical Interpretation of Partial Traces: Two Nonstandard Viewpoints

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.