  Photons carrying orbital angular momentum (OAM) are excellent qudits and are
widely used in several applications, such as long distance quantum
communication, $d$-dimensional teleportation and high-resolution imaging and
metrology. All these protocols rely on quantum tomography to characterise the
OAM state, which currently requires complex measurements involving spatial
light modulators and mode filters. To simplify the measurement and
characterisation of OAM states, here we apply a recent tomography protocol
[Asadian et al., \pra {\bf 94}, 010301 (2016)]. Our scheme for OAM tomography
in $d$ dimensions requires only a set of measurements on a mode qubit, i.e., a
2-dimensional system. This replaces the current complexity of OAM measurements
by the ability to perform generalized Pauli operators $X_d, Z_d$ on OAM states.
Our scheme can be adapted in principle to other degrees of freedom, thus
opening the way for more complex qudit tomography.
