  Entanglement is the basic building block of linear optical quantum
computation, and as such understanding how to generate it in detail is of great
importance for optical architectures. We prove that Bell states cannot be
generated using only 3 photons in the dual-rail encoding, and give strong
numerical evidence for the optimality of the existing 4 photon schemes. In a
setup with a single photon in each input mode, we find a fundamental limit on
the possible entanglement between a single mode Alice and arbitrary Bob. We
investigate and compare other setups aimed at characterizing entanglement in
settings more general than dual-rail encoding. The results draw attention to
the trade-off between the entanglement a state has and the probability of
postselecting that state, which can give surprising constant bounds on
entanglement even with increasing numbers of photons.
