  We perform an experimental investigation of Quantum Discord with Spin-Orbit
X-states. These states are prepared through the incoherent superposition of
different laser beans, where a two-level system is encoded in polarization and
the first-order Hermitian-Gaussian modes, as proposed in Phys. Rev. A
103,0022411 (2022). We characterize different classes of spin-orbit X-states by
performing an all-optical tomography for polarization and first-order
transverse mode degrees of freedom. We also perform a study on the dependence
of Discord with respect to the Fidelity of spin-orbit modes, revealing that
Discord is very sensitive to incoherent noise. Our experimental results align
with the theoretical predictions of Quantum Discord when accounting for the
effect of fidelity. These results reinforce the spin-orbit modes as an
important platform for quantum information processing. On the other hand, the
need of astigmatic optical elements to implement unitary operations required by
quantum information protocols implies in a loss of fidelity and quantum
correlations. Alternative methods to manipulate spin-orbit modes are welcome.
