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A protocol is provided to reconstruct the Wigner function for the motionalstate of a trapped ion via fluorescence detection on another ion in the sametrap. This "sympathetic tomography" of a dark ion without optical transitionssuitable for state measurements is based on the mapping of its motional stateonto one of the collective modes of the ion pair. The quantum state of thisvibrational eigenmode is subsequently measured through sideband excitation ofthe bright ion. Physical processes to implement the desired state transfer andread-out are derived, and the accomplishment of the scheme for different massratios is evaluated.

Sympathetic Wigner function tomography of a dark trapped ion