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We consider the inelastic scattering of two photons from two qubits separated by an arbitrary distance R and coupled to a one-dimensional transmission line. We present an exact, analytical solution to the problem, and use it to explore a particular configuration of qubits that is transparent to single-photon scattering, thus highlighting non-Markovian effects of inelastic two-photon scattering: strong two-photon interference and momentum dependent photon (anti)bunching. This latter effect can be seen as an inelastic generalization of the Hong-Ou-Mandel effect.

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