  We investigate the practicality of the method proposed by Maciel et al.
[Phys. Rev. A. 80, 032325(2009)] for detecting the entanglement of two spatial
qutrits (3-dimensional quantum systems), which are encoded in the discrete
transverse momentum of single photons transmitted through a multi-slit
aperture. The method is based on the acquisition of partial information of the
quantum state through projective measurements, and a data processing analysis
done with semi-definite programs. This analysis relies on generating gradually
an optimal entanglement witness operator, and numerical investigations have
shown that it allows for the entanglement detection of unknown states with a
cost much lower than full state tomography.
