  The density matrix of a two-level system (spin, atom) is usually determined
by measuring the three non-commuting components of the Pauli vector. This
density matrix can also be obtained via the measurement data of two commuting
variables, using a single apparatus. This is done by coupling the two-level
system to a mode of radiation field, where the atom-field interaction is
described with the Jaynes--Cummings model. The mode starts its evolution from a
known coherent state. The unknown initial state of the atom is found by
measuring two commuting observables: the population difference of the atom and
the photon number of the field. We discuss the advantages of this setup and its
possible applications.
