  We introduce a class of communication tests where the task is to communicate
partial ignorance by means of a physical system. We present a full
characterization of the implementations of these tests in the qubit case and
partial results for qudits. A peculiar observation is that two physical systems
with the same operational dimensions may differ with respect to implementations
of these tasks, as is shown to be the case for the qubit and rebit. Finally, we
consider the natural question whether some of the communication tests are more
difficult than others. A new preordering that we call the ultraweak matrix
majorization is presented to answer this question in a theory-independent way.
