Upper bounds on success probabilities in linear optics

We develop an abstract way of defining linear-optics networks designed to perform quantum information tasks such as quantum gates. We will be mainly concerned with the non-linear sign shift (NSS) gate, but it will become obvious that all other gates can be treated in a similar manner. The abstract scheme is extremely well suited for analytical as well as numerical investigations since it reduces the number of parameters for a general setting. With that, we show numerically and partially analytically for a wide class of states that the success probability of generating a NSS gate does not exceed 1/4, which to our knowledge is the strongest bound to date.