  The logarithmic derivative (or, quantum score) of a positive definite density
matrix appearing in the quantum Fisher information is discussed, and its exact
expression is presented. Then, the problem of estimating the parameters in a
class of the Werner-type N-qudit states is studied in the context of the
quantum Cram\'er-Rao inequality. The largest value of the lower bound to the
error of estimate by the quantum Fisher information is shown to coincide with
the separability point only in the case of two qubits. It is found, on the
other hand, that such largest values give rise to the universal fidelity that
is independent of the system size.
