We propose to measure the quantum state of a single mode of the radiation f
ield in a cavity-the signal field-by coupling it via a quantum-non-demoliti
on Hamiltonian to a meter field in a highly squeezed state. We show that qu
antum-state tomography on the meter field using balanced homodyne detection
provides full information about the signal state. We discuss the influence
of measurement of the meter on the signal field. [S1050-2947(99)00801-X].