What does "measurement destroys information" mean? I am reading a paper on quantum cryptography. The author used two facts:

quantum-
information cannot be copied

and

Furthermore, measurements destroy information...

For the first statement, I came to know that due to no-cloning theorem quantum-information can not be copied. What is the rationale behind second statement.
I would be thankful if you can cite some references to read? Is there some kind of theorem for statement two as well?
Thanks

Cross-posted on quantumcomputing.SE
 A: Quantum systems evolve over time in two ways. One way is reversible and preserves information, the other is not.
One way is a process of continuous evolution, in  which the wave function that mathematically describes the system's state evolves according to the Schrodinger equation. This process is deterministic and reversible - if the direction of time in the Schrodinger equation is reversed, the evolution of the wave function simply goes backwards and the original wave function can be (in principle) recovered. So no information is lost here.
The other process is wave function collapse, in which the wave function changes abruptly into an eigenstate. This process is not reversible - there are infinitely many different wave functions that can lead to the same eigenstate when they collapse, so it is not possible to reconstruct the original wave function if all we know is the eventual eigenstate. So wave function collapse involves a loss of information.
A measurement of a quantum system (also called an "observation", but measurement is a more neutral term) causes its wave function to collapse into an eigenstate of the attribute that is being measured. Why ? Because (as far as we know) any accurate and precise measurement process can only return a single value for the attribute that is being measured, not a superposition of multiple values (when we look at Schrodinger's cat it is either dead or alive, not both at the same time). So measurement requires wave function collapse, which in turn results in a loss of information about the original wave function. Hence "measurement destroys information".
Note that there are some interpretations of quantum mechanics (such as the many worlds interpretation) in which wave function collapse does not absolutely destroy information, but only limits the information to which we (in our "world") have access to.
