The efficient manipulation, sorting, and measurement of optical modes and
single-photon states is fundamental to classical and quantum science. Here, we
realise simultaneous and efficient sorting of non-orthogonal, overlapping
states of light, encoded in the transverse spatial degree of freedom. We use a
specifically designed multi-plane light converter (MPLC) to sort states encoded
in dimensions ranging from d=3 to d=7. Through the use of an auxiliary
output mode, the MPLC simultaneously performs the unitary operation required
for unambiguous discrimination and the basis change for the outcomes to be
spatially separated. Our results lay the groundwork for optimal image
identification and classification via optical networks, with potential
applications ranging from self-driving cars to quantum communication systems
