All-optical turbulence mitigation for free-space quantum key distribution using stimulated parametric down-conversion

TL;DR

The paper tackles turbulence-induced distortions in free-space, high-dimensional QKD by introducing StimPDC-based all-optical phase-conjugation to compensate spatial-mode distortions. It develops a theoretical framework linking QER, basis structure (MUBs), and stimulus-beam geometry, and shows that degenerate StimPDC carries the turbulence phase-conjugate to cancel distortions. Through numerical split-step simulations across turbulence strengths and dimensions and a proof-of-principle experiment, the approach maintains QER below the security threshold and improves fidelity and secure key rates relative to standard prepare-and-measure schemes. The work demonstrates a fast, channel-agnostic method for robust free-space quantum communication with potential extensions to quantum imaging and metrology.

Abstract

In this work, we propose and demonstrate a turbulence-resilient scheme for free-space quantum communication. By leveraging the phase conjugation property of stimulated parametric down-conversion, our scheme enables all-optical dynamic correction of spatial-mode distortion induced by atmospheric turbulence, thereby enhancing the secure key rate in high-dimensional quantum key distribution. We develop a theoretical model that provides detailed guidelines for selecting the optimal basis and spatial properties needed to maximize the efficiency of the proposed scheme. Both numerical simulations and experimental results show that, even under strong turbulence, our scheme can reduce the quantum error rates well below the security threshold. These results highlight the potential of nonlinear optical approaches as powerful tools for robust quantum communication in realistic free-space environments. Our work could have important implications for the practical implementation of secure quantum channels over long free-space distances.

Figures (8)

• Figure 1: a) Energy level description of StimPDC. b) StimPDC scheme: Bob sends a Gaussian beam through a turbulent transmission channel to probe the turbulence, and thereby acquires phase distortions. Alice pumps a thin nonlinear crystal with a laser beam encoded with the spatial mode she wants to transmit to Bob. She also seeds the crystal along the signal path with the distorted probe beam. c) As a result, the idler beam carries Alice’s target transmission mode together with the phase-conjugate of the turbulence distortions. For the degenerate situation in which the probe and idler beams have the same wavelength, phase distortions of the returning beam are cancelled, and the intended spatial state is received.
• Figure 2: a) Amplitude and phase structure of the designed MUBs spatial states generated via StimPDC for $d=2$ and $d=5$. b) Fidelity of the spatial basis generated with StimPDC as a function of the ratio $\gamma = w_B / w_A$. We see that for $\gamma=2$ we obtain high fidelities for every element of each basis.
• Figure 3: Optical diameter of the probe beam sent by Bob and the stimulated idler beam generated by Alice, shown for several different probe beam waists: a) 2 cm, b) 3 cm, and c) 4 cm. There exists a specific value of $w_B$ for which the condition $D_B(Z_T) = D_i(Z_T)$ is satisfied, corresponding in this case to scenario b). Although scenario c) satisfies the proposed criterion to a greater extent, it also amplifies the aberrations introduced by turbulence.
• Figure 4: Field simulation results for a) MUB2, $d=2$, $j=1$ and b) MUB1, $d=5$, $j=3$. The target state is shown along with the spatial states distorted by turbulence, and corrected by our scheme. With the StimPDC scheme, it can be observed that the amplitude retains the some aberration as in the P&M case. However, the phase resembles that of the original beam. Panels c) and d) show QER ($Q$) and fidelity loss ($\Delta F$) for the P&M and StimPDC scheme using MUB1 and MUB2 for $d=2$ and $d=5$ obtained with the split-step method. Panels e) and f) present the experimental results. The error bars correspond to the standard error. The shaded area highlights the difference between the QER and the fidelity loss, indicating that the latter does not fully account for the observed crosstalk reduction.
• Figure 5: QER ($Q$) and fidelity loss ($\Delta F$) for the P&M and StimPDC schemes using MUB1 and MUB2 for $d = [2,10]$, obtained with the split-step method for $D_B/r_0 = 3$. For all dimensions, the StimPDC scheme maintains $Q < Q_{\text{max}}$.