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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

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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.

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The definition of information is context dependent and has different interpretations. See How to better define information forum (Physics Insights) As you did not provide a paper, I will assume a very standard context. In general when people talk about information loss in quantum mechanics due to collapse, it is related to irreversibility of collapse.

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).

But if you are told that your system resulted in state 0 after measurement, you cannot retrodict what was the pre-measurement quantum state (one could say that information is lost).

Information in this sense is related to the unitary evolution of the wavefunction and measurements are considered to be non unitary operations (at least to a certain degree of description where you do not care about the environment and measurement apparatus).

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