  The main contribution of this paper is to derive an explicit expression for
the fundamental precision bound, the Holevo bound, for estimating any
two-parameter family of qubit mixed-states in terms of quantum versions of
Fisher information. The obtained formula depends solely on the symmetric
logarithmic derivative (SLD), the right logarithmic derivative (RLD) Fisher
information, and a given weight matrix. This result immediately provides
necessary and sufficient conditions for the following two important classes of
quantum statistical models; the Holevo bound coincides with the SLD Cramer-Rao
bound and it does with the RLD Cramer-Rao bound. One of the important results
of this paper is that a general model other than these two special cases
exhibits an unexpected property: The structure of the Holevo bound changes
smoothly when the weight matrix varies. In particular, it always coincides with
the RLD Cramer-Rao bound for a certain choice of the weight matrix. Several
examples illustrate these findings.
