  A protocol is provided to reconstruct the Wigner function for the motional
state of a trapped ion via fluorescence detection on another ion in the same
trap. This "sympathetic tomography" of a dark ion without optical transitions
suitable for state measurements is based on the mapping of its motional state
onto one of the collective modes of the ion pair. The quantum state of this
vibrational eigenmode is subsequently measured through sideband excitation of
the bright ion. Physical processes to implement the desired state transfer and
read-out are derived, and the accomplishment of the scheme for different mass
ratios is evaluated.
