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I am quite new to this stuff so this question might be trivial. I was reading about bb84 and, as I understood it, after Alice sends $\psi$ Bob chooses a random sequence $b'$ and makes a measurement in either $X$ or $Z$ according to $b'$. After Bob does this he announces that he has received $\psi$ and both him and Alice compare the sequences $b$ and $b'$ discarding the terms for which $b \neq b'$.

What I don't understand: what would be the problem if, after Bob receives $\psi$, he simply announces this fact without choosing $b'$ and making measurements. In this case Alice communicates $b$ to Bob over a public channel and there are no bits to discard.

It seems that Alice has to communicate $b$ to Bob over a public channel in BB84, so why not do it after Bob claims to have received $\psi$?

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What I don't understand: what would be the problem if, after Bob receives $\psi$, he simply announces this fact without choosing $b'$ and making measurements.

At the current state of technology, Bob needs to take a measurement of $\psi$ when he receives it; he can't hold it. It may be that future technology will be able to hold $\psi$ for a nontrivial period of time in an unmeasured quantum state until Alice announces $b$ (and, at that point, Bob cuold then take the appropriate measurement); however, we don't know how to do that now (and it certainly wasn't possible when BB84 was invented).

And, of course, Bob can't measure $\psi$ in both the $X$ and $Z$ basis; that's forbidden by QM (and the security of BB84 relies on that).

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  • $\begingroup$ Hum..nice.. Cheers $\endgroup$ – Francisco Dec 2 '17 at 15:25

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