  Single-photon resolution (SPR) detectors can tell the difference between
incoming wave packets of n and n+1 photons. Such devices are especially
important for linear optical quantum computing with projective measurements.
However, in this paper I show that it is impossible to construct a
photodetector with single-photon resolution when we are restricted to
single-photon sources, linear optical elements and projective measurements with
standard (non-photon-number discriminating) photodetectors. These devices
include SPR detectors that sometimes fail to distinguish one- and two-photon
inputs, but at the same time indicate this failure.
