  Assuming that the parameter dependent evolution, as well as the measurements
that are done for readout, of a quantum system that acts as the probe in a
quantum limited measurement scheme are both fixed, we find the optimal initial
states of the probe that will saturate the quantum Cramer-Rao bound. When the
probe system is itself made of identical, elementary, two-level subsystems or
qubits, we connect the optimal state of the N qubit probe to that of the one
qubit probe. This is done for two different classes of dynamics for the probe
qubits, one of which is entangling while the other is not. We study the
limitations placed on the optimal initial state of the probe and the achievable
measurement uncertainty by restrictions on the readout procedure that is
applied on the probe qubits at the end of the measurement protocol.
