  In this work, we show how to parameterize a density matrix that has an
arbitrary symmetry, knowing the generators of the Lie algebra (if the symmetry
group is a connected Lie group) or the generators of its underlying group (in
case it is finite). This allows to pose MaxEnt and MaxLik estimation techniques
as convex optimization problems with a substantial reduction in the number of
parameters of the function involved. This implies that, apart from a
computational advantage due to the fact that the optimization is performed in a
reduced space, the amount of experimental data needed for a good estimation of
the density matrix can be reduced as well. In addition, we run numerical
experiments and apply these parameterizations to quantum state estimation of
states with different symmetries.
