I have been recently thinking about the nature of the purity of a mixed state. As far as I understand there are two equivalent physical interpretations of mixed states: 1) Ignorance Interpretation: Mixed states arise because of incomplete information concerning the preparation procedure of the state. This interpretation appears to be subjective since the "incomplete information" is to do with the observer and not the state itself. 2) Ensemble Interpretation: Mixed states can represent an ensemble of quantum systems perpared in different pure states. However, mixed states appear in another context: entanglement. That is, by tracing out a subsystem from a pure entangled state of a composite system, one will yield a mixed state for the remaining subsystem. What is the interpretation of this mixed state? It seems to me that in this case, the Ignorance interpretation doesn't really apply since the loss of purity is objective i.e. the subsystem's cannot exist in pure states if the composite system is entangled. In other words, does the purification theorem of mixed states require another physical interpretation?