We introduce the quantum mechanical formalism for treating surface plasmon polariton scattering at an interface. Our developed theory - which is fundamentally different from the analogous photonic scenario - is used to investigate the possibility of plasmonic beamsplitters at the quantum level. Remarkably, we find that a wide-range of splitting ratios can be reached. As an application, we characterize a 50:50 plasmonic beamsplitter and investigate first-order quantum interference of surface plasmon polaritons. The results of this theoretical study show that surface plasmon beamsplitters are able to reliably and efficiently operate in the quantum domain.
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