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 quasiorthogonal) subalgebras of the algebra M4(C) of all 4 × 4 matrices and they are isomorphic to M2(C), then k ≤ 4. In the way to this result, contributions are made to the understanding of the structure of complementary… CONTINUE READING