A SICPOVM is a set of d^2 pure quantum states {|k>} in a d-dimensional Hilbert space,
all whose pairwise inner products have the same magnitude: |<k|j>^2 = 1/(d+1) [for k not equal to j].
SICPOVMs have been constructed analytically (and exactly) in dimensions 2, 3, 4, and 8.
The problem of constructing exact SICPOVMs in other dimensions is (as of 10/13/03) still
unsolved. However, we have numerical solutions in every dimension up to d=45, which satisfy
the former condition up to 1 part in 10^8 or better. This makes us suspect pretty strongly
that exact SICPOVMs do exist in all dimensions! Here, we present the numerical solutions,
as well as the known analytic solutions for d = 2, 3, and 4.

Each of these numerical solutions has the Z_d x Z_d covariance explained in quant-ph/0310075.
Thus, we give only the fiducial state, |0>. In order to generate the full SICPOVM from the
fiducial state, first generate a projective group representation from the generators
S = sum_k{|k><k+1 mod d|} and A = sum_k{exp(2*pi*I*k/d)|k><k|}. Then, each element of this
projective group of d^2 elements will act on |0> to produce a distinct element of the
SICPOVM. Note that when you generate the group, it's projective -- operators which differ
only by a phase are considered identical. Otherwise, you get more than d^2 elements!