Michel Planat, Raymond Aschheim, Marcelo M. Amaral, Klee Irwin (2020)
A popular account of the mixing patterns for the three generations of quarks and leptons is through the characters κ of a finite group G. Here we introduce a d-dimensional Hilbert space with d=cc(G), the number of conjugacy classes of G. Groups under consideration should follow two rules, (a) the character table contains both two- and three-dimensional representations with at least one of them faithful and (b) there are minimal informationally complete measurements under the action of a d-dimensional Pauli group over the characters of these representations. Groups with small d that satisfy these rules coincide in a large part with viable ones derived so far for reproducing simultaneously the CKM (quark) and PNMS (lepton) mixing matrices. Groups leading to physical CP violation are singled out.
