  In connection with optimal state determination for two qubits, the question
was raised about the maximum number of pairwise complementary reductions. The
main result of the paper tells that the maximum number is 4, that is, if A1,
A2,... Ak are pairwise complementary (or quasi-orthogonal) subalgebras of the
algebra of all 4x4$ matrices and they are isomorphic to the algebra of all 2x2
matrices, then k is at most 4. In the way to this result, contributions are
made to the understanding of the structure of complementary reductions.
