  We address estimation of one-parameter unitary gates for qubit systems and
seek for optimal probes and measurements. Single- and two-qubit probes are
analyzed in details focusing on precision and stability of the estimation
procedure. Bayesian inference is employed and compared with the ultimate
quantum limits to precision, taking into account the biased nature of Bayes
estimator in the non asymptotic regime. Besides, through the evaluation of the
asymptotic a posteriori distribution for the gate parameter and the comparison
with the results of Monte Carlo simulated experiments, we show that asymptotic
optimality of Bayes estimator is actually achieved after a limited number of
runs. The robustness of the estimation procedure against fluctuations of the
measurement settings is investigated and the use of entanglement to improve the
overall stability of the estimation scheme is also analyzed in some details.
