  The fundamental gates of linear optics quantum computation are realized by
using single photons sources, linear optics and photon counters. Success of
these gates is conditioned on the pattern of photons detected without using
feedback. Here it is shown that the maximum probability of success of these
gates is typically strictly less than 1. For the one-mode non-linear sign
shift, the probability of success is bounded by 1/2. For the conditional sign
shift of two modes, this probability is bounded by 3/4. These bounds are still
substantially larger than the highest probabilities shown to be achievable so
far, which are 1/4 and 2/27, respectively.
