High-Rate Free-Running Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution with Classified Distillation

Abstract

Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) eliminates detector side-channel attacks and avoids reference-frame calibration. While its feasibility has been widely demonstrated, existing implementations typically assume fixed or slowly drifting reference-frame misalignment, conditions rarely satisfied outside the laboratory. In realistic environments, rapid and free-running reference-frame variations can severely degrade both the key rate and transmission distance of conventional RFI-MDI-QKD. Here we propose a free-running RFI-MDI-QKD protocol that maintains high-rate key generation under rapid reference-frame variations. By introducing a classification-distillation method that reclassifies total detection events, secure keys can be extracted without modifying the experimental setup. Our protocol achieves a key rate more than nine times higher than the best previous RFI-MDI-QKD scheme and tolerates channel losses exceeding 24 dB, where earlier approaches fail. These results enable practical quantum key distribution on mobile platforms, including satellite-to-ground links and airborne nodes.

Figures (4)

• Figure 1: The schematic diagram of the proposed free-running RFI-MDI-QKD scheme. The scheme consists of four main stages: physical communication, data classification, key estimation, and post-processing. $S_i$ denotes the $i$-th subset obtained by dividing the total dataset according to the preset time interval $t$ and performing basis sifting, where $i=1,2,...,n$. $E_{lr,i}^{X X}$ represents the QBER corresponding to the intensity pair $lr$ selected by Alice and Bob in the $\mathit{XX}$ basis of subsets $S_{i}$. $\rho_{i}$ represents the classification parameter associated with the QBER of subset $S_i$. $m$ denotes the optimal number of partition intervals, and $\rho$ is the optimal initial point of the interval. $\Delta_j$ denotes the $j$-th interval obtained by partitioning $\left [ 0,\pi \right )$ into $m$ intervals, where $j=1,2,...,m$. $D_j$ denotes the dataset composed of all subsets $S_i$ contained within the sub-interval $\Delta_j$. $K_{S,j}$ represents the raw key extracted from dataset $D_j$, and $L_{j}$ denotes the secure keys extracted from dataset $D_j$.
• Figure 2: Performance comparison between the proposed free-running RFI-MDI-QKD (FR) scheme and the original RFI-MDI-QKD (OR) scheme under data-acquisition time ($T$) and reference-frame drift rates $(\omega_{RF})$. The solid and dashed lines represent the secret key rates of RF and OR schemes, respectively. In this simulation, both the dataset size $m$ and $\rho_{0}$ are optimized. (a) When $\omega _ {RF}=0$ rad/s corresponds to the fixed reference frame, the secret key rate achieved by the proposed scheme is consistent with that of the original scheme. (b) When $\omega_{\mathrm{RF}} = 3.3\times 10^{-2}$ rad/s corresponds to laboratory reference-frame drift, the accumulated drift of the reference frame increasingly degrades the SKR of the original scheme as the data-acquisition time grows. In particular, once the acquisition time exceeds 50 s, the proposed scheme begins to exhibit significant advantages. (c) When $\omega_{\mathrm{RF}} = 10$ rad/s corresponds to actual buried optical fiber drift, the accumulated drift angle for all considered acquisition times surpasses the critical threshold, causing the original scheme to fail to generate any SKRs, whereas the proposed scheme still generates substantial SKRs.
• Figure 3: Experimental setup of RFI-MDI-QKD. LD, laser diode; Filter, bandwidth-variable tunable filter; VOA, variable optical attenuator; PBS, polarization beam splitter; BS, beam splitter; PM, phase modulator; POL, polarization modulator; $45^{\circ }$ PBS, polarizing beam splitter with $45^{\circ }$ rotation from the optical axis; CIR, circulator; AMZI, asymmetric Mach-Zehnder interferometer; DL, delay line; PC, polarization controller; SNSPD, superconducting nanowire single-photon detector.
• Figure 4: SKRs with different transmission loss. The solid and dashed lines represent the secret key rates of free-running (FR) and original (OR) schemes, respectively. The asterisks and diamonds denote experimental results of the FR and OR schemes with transmission loss of 20 dB (including 5 km fiber) at $N_{tot} = 2\times 10^{11}$ and $\omega_{RF} = 3.93\times 10^{-4}$ rad/s. The upright triangles and squares denote experimental results of the FR and OR schemes with transmission loss of 20 dB at $N_{tot} = 1\times 10^{12}$ and $\omega_{RF} = 1.60\times 10^{-3}$ rad/s. The inverted triangles and circles denote experimental results of the FR and OR schemes with transmission loss of 24 dB at $N_{tot} = 1\times 10^{12}$ and $\omega_{RF} = 3.14\times 10^{-4}$ rad/s.