  We describe a method to perform any generalized purity-preserving measurement
of a qubit with techniques tailored to superconducting systems. First, we
consider two methods for realizing a two-outcome partial projection: using a
thresholded continuous measurement in the circuit QED setup, or using an
indirect ancilla qubit measurement. Second, we decompose an arbitrary
purity-preserving two-outcome measurement into single qubit unitary rotations
and a partial projection. Third, we systematically reduce any multiple-outcome
measurement to a sequence of such two-outcome measurements and unitary
operations. Finally, we consider how to define suitable fidelity measures for
multiple-outcome generalized measurements.
