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.
@article{arxiv.1301.2123,
title = {Optimal quantum tomography of permutationally invariant qubits},
author = {A. B. Klimov and G. Bjork and L. L. Sanchez-Soto},
journal= {arXiv preprint arXiv:1301.2123},
year = {2015}
}