Temporal quantum eraser: Fusion gates with distinguishable photons

Linear-optics gates, the enabling tool of photonic quantum information processing, depend on indistinguishable photons, as they harness quantum interference to achieve nonlinear operations. Yet the required indistinguishability is related to the symmetry of the multiphoton wavefunction, and does not necessarily imply identical photons. Here we show for the case of two-photon gates that the ideal gate operation can be retrieved if one can guarantee the exchange symmetry of the input photonic state. Specifically, we employ a temporal quantum eraser to allow fusion gates with sources of modally-impure photons: parametric photon pair generation and single-photon extraction by a single quantum emitter. The ability to lift the requirement for identical photons bears considerable potential in linear-optics quantum information processing.