Noise Resilient 1SDIQKD for Practical Quantum Networks

TL;DR

This work extends 1SDI-QKD to realistic quantum channels by incorporating amplitude damping, dephasing, and depolarizing noise, and quantifies their impact on secure key rates and efficiency requirements through steering‑based security criteria. It shows a clear noise hierarchy, where dephasing is most tolerable while amplitude damping and depolarizing noise demand near‑unity detection efficiency for comparable noise levels, and reveals a security–entanglement gap in which secure keys vanish despite substantial residual entanglement. By integrating the BBPSSW entanglement purification protocol, the authors demonstrate that 2–4 purification rounds can restore positive key rates in otherwise insecure regimes, albeit with exponential resource costs that cap practical gains. The combination of noise analysis, purification strategies, and operational regimes provides actionable guidance for deploying 1SDI-QKD over metropolitan networks and informs future work on finite‑key security and repeater‑assisted scale‑up.

Abstract

One-sided device-independent quantum key distribution (1SDI-QKD) offers a practical middle ground between fully device-independent protocols and standard QKD, achieving security with detection efficiencies as low as 50.1\% on the untrusted side. However, prior analyses assumed idealized channels, neglecting realistic noise sources. We extend the 1SDI-QKD framework to include amplitude damping, dephasing, and depolarizing noise, quantifying their impact on secure key rates and efficiency requirements. Our results reveal a clear noise hierarchy: dephasing is most tolerable (secure keys achievable at 70\% efficiency with 30\% noise), while amplitude damping and depolarizing noise dramatically elevate requirements to over 90\%. Crucially, we find that security is lost while substantial entanglement remains (concurrence $C \approx 0.7$--$0.8$), demonstrating that steering violation, not merely entanglement, determines 1SDI-QKD security. To mitigate noise effects, we integrate the BBPSSW entanglement purification protocol, showing that 2--4 rounds can restore positive key rates in otherwise insecure regimes. Our resource overhead analysis reveals that effective key rates peak at moderate purification depths; excessive rounds become counterproductive. These findings establish practical boundaries for deploying 1SDI-QKD over metropolitan-scale quantum networks.

Figures (9)

• Figure 1: Schematic of the one‐sided device‐independent QKD setup. An entangled source prepares the two‐qubit state $\lvert\Psi\rangle$ and distributes one qubit to Alice (trusted) and the other to Bob (untrusted) through a noisy quantum channel characterized by amplitude‐damping $\mathcal{E}_{\mathrm{amp}}$, dephasing $\mathcal{E}_{\mathrm{deph}}$, or depolarizing $\mathcal{E}_{\mathrm{depol}}$ noise.
• Figure 2: Hierarchy of quantum correlations. Nested sets illustrate the strict inclusion relations among different classes of quantum correlations: coherence (outermost) $\supset$ discord $\supset$ entanglement $\supset$ steerability $\supset$ nonlocality (innermost). States exhibiting nonlocality form the most restrictive class, while coherence represents the broadest quantum feature. One-sided device-independent QKD exploits steerability, a strictly intermediate resource between entanglement and nonlocality, enabling security certification without requiring full Bell inequality violation or complete device trust ali2024study.
• Figure 3: Secure key rate $r$ versus Bob's detection efficiency $\eta_B$ under different noise models with noise probabilities $p = 0.0$ (blue), $0.1$ (orange), $0.2$ (green), and $0.3$ (purple). (a) Dephasing noise induces a gradual elevation of the minimum efficiency threshold, maintaining positive key rates at $\eta_B \approx 0.65$ even for $p = 0.3$. (b) Amplitude damping sharply elevates efficiency requirements; at $p = 0.3$, detection efficiencies exceeding 90% are necessary. (c) Depolarizing noise exhibits similar behavior to amplitude damping, with the most stringent efficiency thresholds among all noise models.
• Figure 4: Secure key rate $r$ as a function of noise strength for amplitude damping (blue circles), dephasing (orange squares), and depolarizing (green diamonds) channels at ideal detection efficiency $\eta_B = 1$. Vertical dashed lines indicate critical thresholds where $r \to 0$.
• Figure 5: Secure key rate $r$ versus entanglement angle $\theta$ of the initial state $|\psi(\theta)\rangle$, assuming ideal detection efficiency ($\eta_B = 1$) and no channel noise. The maximum occurs at $\theta = \pi/4$ (maximally entangled state), with key rates vanishing as the state becomes separable.