On SIC-POVMs and MUBs in Dimension 6
  We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions.   An algebraic description of a SIC-POVM in dimension six is given. Furthermore it is shown that several sets of three mutually unbiased bases in dimension six are maximal, i.e., cannot be extended. 
Markus Grassl (IAKS, Universitaet Karlsruhe)