Introduction to Quantum Physics and Information Processing

192 Introduction to Quantum Physics and Information Processing

4. Now Bob creates a string k ∈ s

B

keeping only those the bits positions

where m

B

= 1.

5. Bob publicly declares those bit positions, so that Alice can select those

bits from s

A

.

6. Since Alice encoded only 0, Bob can measure a 1 only when their bases

were not the same. Therefore, if Bob’s bit is k

i

then Alice’s bit in the

same position will be 1 − k

i

. Thus after Alice takes the complement of

her bits, both have a shared key k.

The reason this works is as follows: Alice sending a |li means a 0 and a |

l

i

means a 1. Now Bob randomly decides to use the or H basis. But notice

that when he has used ...