  We address quantum decision theory as a convenient framework to analyze
process discrimination and estimation in qubit systems. In particular we
discuss the following problems: i) how to discriminate whether or not a given
unitary perturbation has been applied to a qubit system; ii) how to determine
the amplitude of the minimum detectable perturbation. In order to solve the
first problem, we exploit the so-called Bayes strategy, and look for the
optimal measurement to discriminate, with minimum error probability, whether or
not the unitary transformation has been applied to a given signal. Concerning
the second problem, the strategy of Neyman and Pearson is used to determine the
ultimate bound posed by quantum mechanics to the minimum detectable amplitude
of the qubit transformation. We consider both pure and mixed initial
preparations of the qubit, and solve the corresponding binary decision
problems. We also analyze the use of entangled qubits in the estimation
protocol and found that entanglement, in general, improves stability rather
than precision. Finally, we take into account the possible occurrence of
different kinds of background noise and evaluate the corresponding effects on
the discrimination strategies.
