The measurement postulate states that whenever we make a quantum measurement, we select (projection) from the general superposition state a single pure state. Thus, as a general quantum state is a mixed state, the measurement postulate is just a rule to turn mixed states to pure states and it can not be described by any unitary operator in general.
By the other hand, in black hole physics, generally speaking, we have in general the opposite case. We can prepare a pure state (or even any entangled state) such as when it approaches the black hole and the event horizon, the atmosphere the semiclassical approach roughly implies that the black hole will be evaporated or, in the firewall gedanken experment, something happens in which either the initial state is a mixed state, it gets cloned or even worse, it is destroyed. This breaks down unitarity unless you give up locality or the equivalence principle. I am being rude (if wrong on general ground, tell me).
Question: are the black hole information paradox (current version) and the postulate of the quantum measurement related somehow or are they independent? After all, both of them seems to imply some conversion of pure to mixed states or even to the degree of entanglement before and after the interaction (in the measurement postulate, the apparatus interact with the quantum object; in the black hole information paradox, the quantum object interacts with the black hole "atmosphere").