  We investigate whether a trade-off relation between the diagonal elements of
the mean square error matrix exists for the two-parameter unitary models with
mutually commuting generators. We show that the error trade-off relation which
exists in our models of a finite dimension system is a generic phenomenon in
the sense that it occurs with a finite volume in the spate space. We analyze a
qutrit system to show that there can be an error trade-off relation given by
the SLD and RLD Cramer-Rao bounds that intersect each other. First, we analyze
an example of the reference state showing the non-trivial trade-off relation
numerically, and find that its eigenvalues must be in a certain range to
exhibit the trade-off relation. For another example, one-parameter family of
reference states, we analytically show that the non-trivial relation always
exists and that the range where the trade-off relation exists is up to about a
half of the possible range.
