Recovery of nonseparability in self-healing vector Bessel beams

One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle, both classically and in the quantum regime. Here we demonstrate that the local entanglement, or nonseparability, between the spatial and polarization degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of nonseparability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.