  Weak measurements are a unique tool for accessing information about weakly
interacting quantum systems with minimal back action. Joint weak measurements
of single-particle operators with pointer states characterized by a
two-dimensional Gaussian distribution can provide, in turn, key information
about quantum correlations which can be of relevance for quantum information
applications. Here we demonstrate that by employing two-dimensional pointer
states endowed with orbital angular momentum (OAM), it is possible to extract
weak values of the higher order moments of single-particle operators, an
inaccessible quantity with Gaussian pointer states only. We provide a specific
example that illustrates the advantages of our method both, in terms of signal
enhancement, and information retrieval.
