  The joint weak value is a counterfactual quantity related to quantum
correlations and quantum dynamics, which can be retrieved via weak
measurements, as initiated by Aharonov and colleagues. In this Rapid
Communication, we provide a full analytical extension of the method described
by Puentes et al. [Phys. Rev. Lett. 109, 040401 (2012)], to extract the joint
weak values of single-particle operators from two-dimensional spatial
displacements of Laguerre-Gauss probe states, for the case of azimuthal index
|l|>1. This method has a statistical advantage over previous ones since
information about the conjugate observable, i.e., the momentum displacement of
the probe, is not required. Moreover, we demonstrate that under certain
conditions, the joint weak value can be extracted directly from spatial
displacements without any additional data processing.
