  We consider the problem of optimally approximating an unavailable quantum
state $\rho $ by the convex mixing of states drawn from a set of available
states $\{ \nu_i\}$. The problem is recast to look for the least
distinguishable state from $\rho $ among the convex set $\sum_i p_i \nu_i$, and
the corresponding optimal weights $\{ p_i \}$ provide the optimal convex
mixing. We present the complete solution for the optimal convex approximation
of a qubit mixed state when the set of available states comprises the three
bases of the Pauli matrices.
