Optical logic down to the single photon level holds the promise of data processing with a better energy efficiency than electronic devices [1]. In addition, preservation of quantum coherence in such logical components could lead to optical quantum logical gates [2–4]. Optical logic requires optical non-linearities to enable photon-photon interactions. Non-linearities usually appear for large intensities, but discrete transitions allow for giant non-linearities operating at the single photon level [5], as demonstrated for a single optical mode with cold atomic gases [6, 7], or single two-level systems coupled to light via a tailored photonic environment [8–13]. However optical logic requires two-mode non-linearities [14, 15]. Here we take advantage of the large coupling efficiency and the broadband operation of a photonic wire containing a semiconductor quantum dot (QD) [16] to implement an all-optical logical component, wherein as few as 10 photons per QD lifetime in one mode control the reflectivity of another, spectrally distinct, mode. Whether classical or quantum, optical communication has proven to be the best choice for long distance information distribution. All-optical data processing has therefore raised much interest in recent years, as it would avoid energy and coherence consuming optics-to-electronics conversion steps. Two-ports operation is a necessary requirement for the implementation of any non-trivial optical data processing. This involves a non-linear interaction between two distinct optical modes. Such a functionality operating at the single photon level can be achieved with a giant cross non-linearity obtained via resonant interactions in an atomic-like system featuring discrete energy levels [5].