Purification of noisy quantum measurements

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 allow one to perfectly measure an observable on a single quantum system for increasing number of inefficient detectors. For measurements of observables with an unbounded spectrum (e.g., photon number and homodyne and heterodyne detection), the purification of noisy quantum measurements can be achieved by preamplification as suggested by Yuen [Opt. Lett. 12, 789 (1987)].