I feel really stupid asking this question, but I just can't figure out why I am wrong. Here goes:
I am giving a lecture about Quantum Cryptography, and as I am studying it again, I don't see why the following attack doesn't work (I am thinking about BB84):
Why can't Eve just use the bits sent to Bob as control in a CNOT, keeping the second bits, and passing on the original qubits unchanged? Then when Bob measures, her qubits collapse to the same state, and by listening to the communication between Alice and Bob, she know everything she needs to know to measure the qubits in the correct basis and get the correct values.
Everywhere I read argues that Eve can't copy the bits because of the no-cloning theorem, but it seems to me that copying the qubits wouldn't help anyway. However this--so it seems to me right now--is even better--by using entanglement, she has exactly what Bob has, and when he measures, he measures her qubits as well.
Does this make sense?
I know this is wrong, but I can't see why.