  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.
