# 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 physics.SE

If you measure a state $$|\psi\rangle = a|0\rangle + b|1\rangle$$, the post-measurement state will be either $$|0\rangle$$ or $$|1\rangle$$ with $$|a|^2$$ and $$|b|^2$$ probability, respectively. The important part here is that the values for $$a$$ and $$b$$ are lost in the post-measurement state and you end up with a basis state $$\{|0\rangle, |1\rangle\}$$ with an amplitude of $$1$$, which is what I guess the author of the paper is referring to. Check out Entropy Gain and Information Loss by Measurements for further information.
If you have a qubit in state $$(|0\rangle +|1\rangle)/\sqrt{2}$$ you can predict the possible measurement outcomes (50% 0 and 50% 1).