  Strong nonlinear interactions between photons enable logic operations for
both classical and quantum-information technology. Unfortunately, nonlinear
interactions are usually feeble and therefore all-optical logic gates tend to
be inefficient. A quantum emitter deterministically coupled to a propagating
mode fundamentally changes the situation, since each photon inevitably
interacts with the emitter, and highly correlated many-photon states may be
created . Here we show that a single quantum dot in a photonic-crystal
waveguide can be utilized as a giant nonlinearity sensitive at the
single-photon level. The nonlinear response is revealed from the intensity and
quantum statistics of the scattered photons, and contains contributions from an
entangled photon-photon bound state. The quantum nonlinearity will find
immediate applications for deterministic Bell-state measurements and
single-photon transistors and paves the way to scalable waveguide-based
photonic quantum-computing architectures.
