Device-independent quantum key distribution over 100 km with single atoms

TL;DR

This work demonstrates device-independent QKD between two single-atom memories over metropolitan-scale fibers by employing SPI-based heralded entanglement and quantum-frequency conversion to telecom wavelengths. A tailored Rydberg-based single-photon-emission protocol suppresses photon-recoil, achieving high-fidelity atom–atom entanglement up to 100 km and a finite-size secure key rate of $0.112$ bits per event at 11 km, with a positive asymptotic rate maintained up to 100 km. Phase stabilization, high-visibility interference, and an integrated QRNG enable robust, self-testing DI-QKD under realistic conditions. The results bridge laboratory DI-QKD demonstrations toward real-world quantum networks and point to scalable extensions via continuous operation, multiplexing, and improved fiber technologies to boost entangling rates and key throughput.

Abstract

Device-independent quantum key distribution (DI-QKD) is a key application of the quantum internet. We report the realization of DI-QKD between two single-atom nodes linked by 100-km fibers. To improve the entangling rate, single-photon interference is leveraged for entanglement heralding, and quantum frequency conversion is used to reduce fiber loss. A tailored Rydberg-based emission scheme suppresses the photon recoil effect on the atom without introducing noise. We achieved high-fidelity atom-atom entanglement and positive asymptotic key rates for fiber lengths up to 100 km. At 11 km, 1.2 million heralded Bell pairs were prepared over 624 hours, yielding an estimated extractable finite-size secure key rate of 0.112 bits per event against general attacks. Our results close the gap between proof-of-principle quantum network experiments and real-world applications.

Figures (15)

• Figure 1: Experimental architecture for device-independent QKD with neutral-atom quantum memories. (A) Overview of DI-QKD system. Two single-atom nodes (Alice and Bob) emit photons that are converted to the telecom band and interfered at Charlie for heralded entanglement. Random inputs $X_i$, $Y_i$ set measurement bases, and outputs $A_i$, $B_i$ are recorded. An authenticated public classical channel connects Alice and Bob for post-processing. (B) Single-atom node schematic. The hyperfine qubits are manipulated via Raman pulses with electro-optic modulators (EOM) setting the measurement bases. A pair of Rydberg lasers drive the RSPE process for single-photon generation. Four in-vacuo lenses (NA = 0.52) collect fluorescence, with C2-C4 coupled to SPCMs for fluorescence detection and C1 coupled into a single-mode fiber to the QFC module. (C) QFC module. The 780 nm photons are converted to 1315 nm in an RPE-PPLN waveguide, driven by a 1917 nm pump and followed by spectral filtering. An AOM gates the pump to suppress noise. (D) Temporal filtering. The pump is switched on only during photon arrival to suppress excitation-pulse noise. (E) Fluorescence detection. Histogram of SPCM counts with 35 $\mu$s exposure; dashed line marks the discrimination threshold (4 counts). The inset shows photon-counting statistics from 5-ms weak imaging with single-lens collection (C4), yielding a state discrimination fidelity above 99.9%. (F) Long-lived quantum memories. Qubit coherence versus storage time for Hahn-echo (blue), XY-4 (green), and transferring qubits into clock basis and then applying XY-8-32 sequence (purple).
• Figure 2: Single-photon generation and characterization. (A) Rydberg-based single photon emission (RSPE) scheme. The qubit state $\ket{\uparrow}$ is coherently excited to a long-lived Rydberg state $\ket{r}$ via a two-photon transition ($k_1$, $k_2$). After a controllable delay $T$, the atom is de-excited to the excited state $\ket{e}$ ($k_3$), from which spontaneous decay produces a single photon $(k_4)$. (B) Temporal profile of detected photons. The 780 nm Rydberg excitation pulses (red region) are well separated from the single-photon signal (blue peak); The noise level is suppressed to below $2\times10^{-8}$ in normalized units. (C) Single-photon interference fringes obtained by scanning the phase of the interferometer and detecting the normalized single-photon counts from two output channels. Blue and orange points correspond to two SNSPD channels, respectively. Solid curves represent sinusoidal fits to the measured data. Error bars represent one standard deviation assuming Poissonian statistics. (D) Hong-Ou-Mandel (HOM) interference of independently emitted photons. Relative coincidence counts for parallel (orange) and perpendicular (blue) polarizations are shown as a function of detection time delay.
• Figure 3: Heralded entanglement over long-distance telecom fiber. (A) Experimental sequence for atom-atom entanglement. Atom–photon entanglement (APE) is first generated at each node, and the photons interfere at Charlie to herald entanglement. Memory coherence is preserved using dynamical decoupling. The entangled state is analyzed by applying single-qubit rotations $R_\theta(\varphi)$ followed by push-out detection. (B) Heralded entanglement event rate versus total fiber length $L$. Purple squares denote measured rates with SPI Scheme, and brown line denotes the expected rate for two-photon interference scheme at the same repetition rate, which scales with $0.5\eta_A\eta_B$ and falls more steeply with distance. (C) Entanglement characterization at 11 km. Top: parity oscillations for the $\ket{\psi^{+}}$ (teal) and $\ket{\psi^{-}}$ (blue-gray) states versus interferometer phase, with sinusoidal fits (solid curves). Bottom: measured populations in the $\hat{Z}\hat{Z}$ basis, with statistical uncertainties below $10^{-3}$. (D) Entanglement fidelity versus $L$. Stars: this work (labels indicate the optimized excitation probability $\alpha$ at each $L$); points: prior demonstrations (individual atoms van2022entanglingzhang2022device, NV/SIV centers knaut2024entanglementstolk2024metropolitanhensen2015loophole, trapped ions krutyanskiy2023entanglement, atomic ensembles liu2024creation). Fidelities remain $> 0.9$ up to 100 km, satisfying DI-QKD requirements.
• Figure 4: DI-QKD over 11 km with finite-size security.A–C, Experimental performance metrics. A, Quantum bit error rate (QBER); B, CHSH Bell parameter $S$ versus accumulated events, with shaded bands indicating one standard deviation. C, Wall-clock time to accumulate events. D, Finite-size secure key rate $R$ versus the number of rounds $n$ with a soundness error of $\epsilon_{\mathrm{snd}} = 10^{-5}$ and optimized Bell-test fractions ($\gamma_A = 0.26$, $\gamma_B = 0.13$). evaluated using two methods (original EAT and Rényi EAT). Cyan: original EAT; orange: Rényi EAT; dashed: asymptotic bound. At $n = 1.208\times10^{6}$ (dotted line), the Rényi EAT yields $R = 0.112$ bits per event (0.06 bit/s), while the original EAT gives $R = 0.034$ bits per event.
• Figure 5: Device-independent QKD performance over metropolitan-scale fiber.A, Quantum bit error rate (QBER) versus fiber length, increasing from $2.85\%$ at 11 km to $7.16\%$ at 100 km. B, CHSH violation S as a function of fiber length, remaining well above the classical bound of 2 for all distances tested, thus confirming sustained nonlocal correlations. C, Asymptotic secret key rate with $\gamma = 10^{-3}$, showing secure key generation maintained up to 100 km. Error bars represent one standard deviation from Poissonian counting statistics.