JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 46, 10 (2013)
We study the problem of constructing mutually unbiased bases in dimension 6. This approach is based on an efficient numerical method designed to find solutions to the quantum state reconstruction problem in finite dimensions. Our technique suggests the existence of previously unknown symmetries in Karlsson’s non-affine family K_2^6 which we confirm analytically. Also, we obtain strong evidence that not more than three mutually unbiased bases can be constructed from pairs which contain members of some non-affine families of complex Hadamard matrices.