Topological Robustness of Orbital Angular Momentum Entanglement in Stochastic Channels

Orbital angular momentum (OAM) entanglement gives access to multiple qubit and high dimensional Hilbert spaces but is unfortunately susceptible to disturbance, decaying in real-world noisy channels. Here, we show that an underlying topology arising from OAM entanglement remains robust to such channels, which we demonstrate using atmospheric turbulence-exemplary of stochastic or chaotic media. Using a quantum channel with various turbulence strengths, we find that the OAM topological observable is preserved even though the OAM itself is shown to be highly sensitive to the turbulence. We show this is true for mixed states too, with the OAM topology intact even as the purity of the state decreases due to decoherence. Our Letter offers a new perspective on harnessing OAM entanglement in noisy channels, and may easily be extended to other spatial bases, degrees of freedom, and complex channels.