  We revisit the maximum-entropy inference of the state of a finite-level
quantum system under linear constraints. The constraints are specified by the
expected values of a set of fixed observables. We point out the existence of
discontinuities in this inference method. This is a pure quantum phenomenon
since the maximum-entropy inference is continuous for mutually commuting
observables. The question arises why some sets of observables are distinguished
by a discontinuity in an inference method which is still discussed as a
universal inference method. In this paper we make an example of a discontinuity
and we explain a characterization of the discontinuities in terms of the
openness of the (restricted) linear map that assigns expected values to states.
