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Coincidence Landscapes for Three-Channel Linear Optical Networks

We use permutation-group methods plus SU(3) group-theoretic methods to determine the action of a three-channel passive optical interferometer on controllably delayed single-photon pulse inputs to each channel. Permutation-group techniques allow us to relate directly expressions for rates and, in particular, investigate symmetries in the coincidence landscape. These techniques extend the traditional Hong-Ou-Mandel effect analysis for two-channel interferometry to valleys and plateaus in three-channel interferometry. Our group-theoretic approach is intuitively appealing because the calculus of Wigner $D$ functions partially accounts for permutational symmetries and directly reveals the connections among $D$ functions, partial distinguishability, and immanants.