  The practical implementation of free-space quantum information tasks requires
entanglement to be sustained over long distances and in the presence of
turbulent and noisy environments. The transverse position-momentum entanglement
of photon pairs produced by parametric down-conversion has found several uses
in quantum information science, however, it is not suitable for applications
involving long-distance propagation as the entanglement decays very rapidly
when photons propagate away from their source. Entanglement is lost after a few
centimetres of propagation, and the effect becomes even more pronounced in
turbulent environments. In contrast, in this article, we show that entanglement
in the angle-orbital angular momentum (OAM) bases exhibits a remarkably
different behaviour. As with the position-momentum case, initially, the
angle-OAM entanglement decays with propagation, but as the photons continue to
travel further from the source, the photons regain their strongly correlated
behaviour, and the entanglement returns. We theoretically and experimentally
demonstrate this behaviour and show that entanglement returns even in the
presence of strong turbulence. The only effect of turbulence is to increase the
propagation distance for revival, but once revived, the two photons remain
entangled up to an arbitrary propagation distance. This work highlights the
role that OAM-angle entanglement will play in applications where quantum
information is shared over long distances.
