  Photonic quantum systems are among the most promising architectures for
quantum computers. It is well known that for dual-rail photons effective
non-linearities and near-deterministic non-trivial two-qubit gates can be
achieved via the measurement process and by introducing ancillary photons.
While in principle this opens a legitimate path to scalable linear optical
quantum computing, the technical requirements are still very challenging and
thus other optical encodings are being actively investigated. One of the
alternatives is to use single-rail encoded photons, where entangled states can
be deterministically generated. Here we prove that even for such systems
universal optical quantum computing using only passive optical elements such as
beam splitters and phase shifters is not possible. This no-go theorem proves
that photon bunching cannot be passively suppressed even when extra ancilla
modes and arbitrary number of photons are used. Our result provides useful
guidance for the design of optical quantum computers.
