[softy54534]

In the many-worlds interpretation, there is no loss of information when a quantum system is measured. When the quantum state interacts with the macroscopic state, there is a one-to-one correspondence between the superposition of macroscopic states and the quantum state (the superposition of its basis eigenstates). It is only because we only see one of the eigenstates of the macroscopic state corresponding to one of the eigenstates of the quantum states that the information associated with the other eigenstates that we don't see is lost. We don't see the other eigenstates because they are orthogonal and do not interfere with the eigenstate that we do see.

Note that quantum mechanics is linear:

If y ® Y and f ® F, then:

ay + bf ® aY + bF