Experimental investigation of quantum discord in spin-orbit <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> states

We perform an experimental study of quantum discord on spin-orbit modes of an intense laser beam, analogous to different X states. These modes are prepared through the incoherent superposition of different intense laser beams, encoding a two-qubit system in both polarization and the first-order Hermite-Gaussian modes [as proposed in Phys. Rev. A 103, 022411 (2021)]. We characterize these modes by using all-optical tomography and calculated entropic quantum discord. Remarkably, even for high-fidelity mode reconstruction, the computation of quantum discord showed significant deviations from theoretical expectations. Then, we proposed a simple model based on noisy measurements that showed a small degradation of the fidelity of the output modes, giving rise to the strong deviation of the discord. Our results, both experimental data and the theoretical predictions, demonstrate good agreement.