The new Entropic Information approach
Black Hole as whole quantum system
Throw in a black hole a quantum system in a pure state and waits for some amount of time until the hole has evaporated, we end up with is a thermal state.
A pure quantum state is a state which can be described by a single ket vector and of which the entropy is zero because there is no uncertainty in this state.
A thermal state is a mixed state (described quantum mechanically by a density matrix rather than a wave function).
We are face to a system which converts a pure state into a mixed state.
During the transformation between a mixed state and a pure state, some information is lost. But prime directive of quantum mechanics indicate that quantum evolution should be unitary and, thus, information and entropy should be conserved.
In fact, if we had a very complex quantum system which starts in a pure state, it will appear to thermalize and will emit radiation that is very close to thermal. In particular, in the early stages, if we computed the von Neumann entropy of the emitted radiation it would be almost exactly thermal because the radiation is entangled with the quantum system.
As a side note, we must take in account that the black Hole information paradox can be established using the standard Copenhagen method of keeping the system separate from the measuring device.
The black hole information paradox is independent of the quantum measurement problem.
As such we can discuss the solutions to the information paradox without committing to any particular interpretation of quantum mechanics.