We derive a set of criteria to decide whether a given projection measurement can be, in principle, exactly implemented solely by means of linear optics. The derivation can be adapted to various detection methods, including photon counting and homodyne detection. These criteria enable one to obtain no-go theorems easily for the exact distinguishability of orthogonal quantum states with linear optics, including the use of auxiliary photons and conditional dynamics.

• Received 16 April 2003

DOI:https://doi.org/10.1103/PhysRevA.69.012302