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.
Help?
Actually, the real security
Actually, the real security of BB84 lies in a bit of random guesswork combined with error correction. It is assumed that Eve does gain some information but through error correction it can be shown that Alice and Bob can correct down to the point that Eve has zero usable information. An awesome reference on this, particularly from a pedagogical point of view, is the book Protecting Information: From Classical Error Correction to Quantum Cryptography by Susan Loepp and Bill Wootters and published by CUP.