  We derive an expression for a density operator estimated via Bayesian quantum
inference in the limit of an infinite number of measurements.
  This expression is derived under the assumption that the reconstructed system
is in a pure state. In this case the estimation corresponds to an averaging
over a generalized microcanonical ensemble of pure states satisfying a set of
constraints imposed by the measured mean values of the observables under
consideration. We show that via the ``purification'' ansatz, statistical
mixtures can also be consistently reconstructed via the quantum Bayesian
inference scheme. In this case the estimation corresponds to averaging over the
generalized canonical ensemble of states satisfying the given constraints, and
the reconstructed density operator maximizes the von Neumann entropy (i.e.,
this density operator is equal to the generalized canonical density operator
which follows from the Jaynes principle of maximum entropy). We study in detail
the reconstruction of the spin-1/2 density operator and discuss the logical
connection between the three reconstruction schemes, i.e., (1) quantum Bayesian
inference, (2) reconstruction via the Jaynes principle of maximum entropy, and
(3) discrete quantum tomography.
