Protecting the entanglement of twisted photons by adaptive optics

We study the efficiency of adaptive optics (AO) correction for the free-space propagation of entangled photonic orbital-angular-momentum (OAM) qubit states to reverse moderate atmospheric turbulence distortions. We show that AO can significantly reduce crosstalk to modes within and outside the encoding subspace and thereby stabilize entanglement against turbulence. This method establishes a reliable quantum channel for OAM photons in turbulence, and it enhances the threshold turbulence strength for secure quantum communication by at least a factor 2.

Figure 1

Sketch of the setup: An entangled photon source (EPS) in Alice's laboratory produces a pair of entangled twisted photons. One photon is kept in Alice's laboratory, while the other is sent to Bob through a free-space channel. A Gaussian beacon (blue arrow) travels along the same path as the twisted photon (red spiral arrow). The AO system mitigates phase distortions of the twisted photons based on the wavefront sensor (WFS) measurements of the beacon.

Figure 2

Validation of the simulation routine with a single phase screen: (a) concurrence and (b) trace of the final density matrix. Solid lines correspond to analytical results, while points refer to numerical data. Error bars in (a) are obtained via error propagation from the standard deviation of the mean on the elements of $\rho$ (see Appendix pp2). In (b), the standard deviation of the mean is smaller than the size of the symbols.

Figure 3

Concurrence $C$ (5) (a)–(c) and trace $\mathcal{N}$ (d)–(f) of the disorder-averaged and projected biphoton output state $\rho$ plotted against the effective turbulence strength $w_0/r_0$ for different degrees of adaptive optics compensation: (a), (d) without compensation, (b), (e) ideal, and (c), (f) tip-tilt AO. Note the different scale of the $y$ axis in (b). Error bars in (a)–(c) are obtained via error propagation from the standard deviation of the mean on the elements of $\rho$ (see Appendix pp2). In (d)–(f) the standard deviation of the mean is smaller than the size of the symbols.

Figure 4

Cross-talk-induced detection error contribution $R$, see Eq. (6), to the quantum bit error rate as a function of $w_0/r_0$: (a) without turbulence compensation, (b) with an ideal, and (c) with tip-tilt AO. Dashed horizontal lines in (a,c) indicate the security threshold of 11% [33] [note the different scale of the $y$ axis in (b)]. Error bars represent the standard deviation of the mean.