The general impossibility of determining the state of a single quantum
system is proved for arbitrary measuring schemes, including a success
ion of measurements. Some recently proposed methods are critically exa
mined. A scheme for tomographic measurements on a single copy of a rad
iation field is devised, showing that the system state is perturbed ho
wever weak the system-apparatus interaction is, due to the need of pre
paring the apparatus in a highly ''squeezed'' state.