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The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalge-bras. The concept of complementarity is extended to non-commutative subalge-bras. Complementary decompositions of a 4-level quantum system are described and a characterization of the Bell basis is obtained.(More)
In this paper, we examine a generalization of the symmetric informationally complete POVMs. SIC-POVMs are the optimal measurements for full quantum tomography, but if some parameters of the density matrix are known, then the optimal SIC POVM should be orthogonal to a subspace. This gives the concept of the conditional SIC-POVM. The existence is not known in(More)
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