  Mutually unbiased bases determine an optimal set of measurements to extract
complete information about the quantum state of a system. However, quite often
a priori information about the state exist, making some of the measurement
bases superfluous. This is, for example, the case when multiqubit states belong
to the permutationally invariant subspace. In this paper we derive the minimal
sets of mutually unbiased bases needed to tomographically reconstruct such
states.
