Noninformative prior of the quantum statistical model in the qubit system*

In quantum process tomography, we often encounter a parametric family of qubits with less symmetry and estimate the parameter from experimental data. If we use Bayes estimates, then we have to choose a default probability distribution over the parameter space, which is called a noninformative prior. While the effect of the prior becomes smaller with the large amount of data, the choice of the noninformative prior based on a certain criterion has been of theoretical interest. In this talk, we consider a suitable definition of a noninformative prior in a general parametric family of qubits.
In the classical Bayesian statistics, there is no universal criterion and still there are many works on the choice of a noninformative prior like the famous Jeffreys prior. The most famous one is Bernardo's criterion, which deals with the maximization of the mutual information. However, its formal extension is troublesome because the quantum relative entropy between two pure states diverges.
Recently the author proposed another way based on the quantum detection game, which is well-defined in pure-states model. In this talk, as further development, we extend the argument to general qubit models, which yields Bures geometry.