Recall that in the Bennett–Brassard key distribution scheme, after Alice and Bob have obtained bit strings that ideally are supposed to be identical, they have to do some further processing to make sure they end up with strings that really are identical. Our first goal in this chapter is to show how they can do this.

As you might expect, we will use error-correcting codes of the sort we have been discussing in the preceding chapter. However, the way we use error-correcting codes in quantum key distribution is not quite the same as in classical communication. Normally, one corrects errors by encoding one's message into special codewords that are sufficiently different from each other that they will still be distinguishable after passing through a noisy channel. But in quantum key distribution the “noise” of the channel might actually be the effect of an eavesdropper who is free to manipulate the signals sent by Alice. Ordinary error correction is not designed for such a setting. So instead of using codewords to encode the original transmission, we wait until all the bits have been sent and then use an error-correcting code after the fact. In this respect error correction in quantum key distribution is similar to the use of an error-correcting code in the “hat problem” discussed at the end of Chapter 4. There also, the error-correcting code is applied only after all the data – in that case the vector of hat colors – has been generated and conveyed to the participants.