EXPLORING A NEW POST-SELECTION CONDITION FOR EFFICIENT LINEAR OPTICS COMPUTATION

Recently, it has been shown that fundamental gates for theoretically efficient quantum information processing can be realized by using single photon sources, linear optics and photon counters. One of these fundamental gates is the NS-gate, that is, the one-mode non-linear sign shift. In this work, firstly, we prove by an elementary and rigorous proof that the upper bound of success probability of NS-gates with only one helper photon and an undefined number of ancillary modes is bounded by 0.25. Secondly, we explore the upper bound of the success probability of the NS-gate with a new post-selection measurement. The idea behind this new post-selection measurement is to condition the success of NS-gate transformation to the observation of only one helper photon in whichever of the output modes.