  We consider the problem of improving noisy quantum measurements by suitable
preprocessing strategies making many noisy detectors equivalent to a single
ideal detector. For observables pertaining to finite-dimensional systems (e.g.
qubits or spins) we consider preprocessing strategies that are reminiscent of
quantum error correction procedures and allows one to perfectly measure an
observable on a single quantum system for increasing number of inefficient
detectors. For measurements of observables with unbounded spectrum (e.g. photon
number, homodyne and heterodyne detection), the purification of noisy quantum
measurements can be achieved by preamplification as suggested by H. P. Yuen
[1].
