Bohr placed complementary bases at the mathematical centre point of his view
of quantum mechanics. On the technical side then my question translates into
that of classifying complex Hadamard matrices. Recent work (with Barros e Sa)
shows that the answer depends heavily on the prime number decomposition of the
Hilbert space. By implication so does the geometry of quantum state space.Comment: 6 pages; talk at the Vaxjo conference on Foundations of Probability
and Physics, 201
