Complementarity and the algebraic structure of 4-level quantum systems
  The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras. Complementary decompositions of a 4-level quantum system are described and a characterization of the Bell basis is obtained. 
D. Petz, A. Szanto, M. Weiner