, U with X. Comparing the top and bottom lines of the table, we notice that the right choices give Bob information bits that are always correct with respect to Alice' initial sequence. In the other case of wrong basis choice, Bob's information bits are inherently random and, therefore, not correlated with those of Alice's sequence. 25.9 A secure photon communication channel Table 25.8 Alice's 16-bit and corresponding photon-state sequence, Bob's choice of Xand Z measurement basis, and the outcome of the measurements in terms of eigenvalues and corresponding 1 or 0 information bits. The outcomes shown in bold correspond to Bob's accidentally correct choices of measurement basis. Alice's bit sequence Alice's photon state sequence uun I Bob's measurement basis choice Bob's measurement outcome (eigenvalue) +1+1-1 +1-1+1+1 -1-1+1+1 -1-1-1+1 Bob's measurement outcome (bit) Bob's next move is to communicate to Alice, using a public channel like telephone or email, not the bits he has measured, but his measurement-basis sequence, namely from Table 25.8: ZXZX XZZX XZXX XXZZ. Such information will tell Alice Bob's right choices in the measurement, since she is the only one to know how she has coded the photon polarizations. She then uses the same public channel to give Bob her answer, which comes in the form: YesNoNoYes NoYesNoNo NoNoYesNo Yes Yes No Yes. This information tells Bob where his measurements were right and, therefore, which information bits are valid and which other ones are to be discarded. ¹9 Thus, Bob and Alice keep as valid the following bit sequence (- meaning discarded bit): -0/-0--/--1-/00-1=1001001, which amounts to nine valid bits altogether. Since the probability of Bob choosing the right measurement basis is 50%, it is clear that for longer sequences Bob would obtain about 50% valid bits. Thus, if Alice sends a 1000 bit sequence to Bob, the whole operation will result in obtaining a valid bit sequence of a length of nearly 500 bits. Such a sequence can then be used by both Alice and Bob as a shared 