  It has been shown that classes of (minimal asymmetric) informationally
complete POVMs in dimension d can be built using the multiparticle Pauli group
acting on appropriate fiducial states [M. Planat and Z. Gedik, R. Soc. open
sci. 4, 170387 (2017)]. The latter states may also be derived starting from the
Poincar\'e upper half-plane model H. For doing this, one translates the
congruence (or non-congruence) subgroups of index d of the modular group into
groups of permutation gates whose some of the eigenstates are the seeked
fiducials. The structure of some IC-POVMs is found to be intimately related to
the Kochen-Specker theorem.
