  We introduce a type of measurements that generalize the so-called "partial
measurements" performed in recent years with phase qubits. While in the case of
partial measurements it has been demonstrated that one could undo the effect of
the measurement only for non-switching events, we show here that generalized
partial measurements can be reversed probabilistically for both switching and
non-switching events. We calculate the associated Fisher information and
discuss the estimation sensitivity for quantum tomography. Two ways of
implementing this type of measurements with superconducting qubits are
proposed.
