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For questions about quantum algorithms, that is, sequences of quantum gates, operations, and measurements, whose purpose which achieve some goal. Standard examples are Shor's and Grover's algorithms.

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How to prove teleportation does not violate no-cloning theorem?

For a given teleportation process as depicted in the figure, how one can say that teleporting the qubit state $|q\rangle$ has not cloned at the end of Bob's measurement?
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How to prove teleportation does not violate no-cloning theorem?

I.e., if we have the entire initial state is written as follows $$| q \rangle \otimes | \beta_{00} \rangle =(\alpha | 0\rangle+\beta | 1 \rangle ) \otimes \frac{1}{\sqrt{2}}( |00\rangle+| 11 \rangle)$ …
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