I'm approaching the Simon's Algorithm and have troubles with understanding a logic in an introduction.
Above the eq. 6.5.4 they introduce that set S which has 2 elements. As far as I understand, these are: n zeroes (0) and an arbitrary string of n [zeroes and ones] (s). As 6.5.4 suggests, the set S contains vectors which are 'forbidden' for the z (in the sum they indicate that z belongs to s perpendicular which is orthogonal to S). The idea behind introducing that subspace of S is to eliminate kets for which the phase is 0 (s$*$z=1). But if z takes 00..., the bitwise inner product with anything is 0 and it seems to be what we want, so why is it in the 'forbidden' set S?
Could you please bring me back on the right track?