An It-bit string is encoded as a sequence of nonorthogonal quantum sta
tes. The parity bit of that n-bit string is described by one of two de
nsity matrices, rho(0)((n)) and rho(1)((n)), both in a Hilbert space o
f dimension 2(n). In order is to derive the parity bit the receiver mu
st distinguish between the two density matrices, e.g., in terms of opt
imal mutual information. In this paper we find the measurement which p
rovides the optimal mutual information about the parity bit and calcul
ate that information. We prove that this information decreases exponen
tially with the length of the string in the case where the single bit
states are almost fully overlapping. We believe this result will be us
eful in proving the ultimate security of quantum cryptography in the p
resence of noise.