One-Sided Device-Independent Quantum Key Distribution over Noisy Metropolitan Links: Noise Thresholds and Purification-Assisted Recovery

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. This work extends the 1SDI-QKD framework to amplitude damping, dephasing, and depolarizing noise. Results reveal a clear noise hierarchy: dephasing tolerates the most noise before security is lost ($p_{\text{crit}} \approx 0.50$ versus 0.449 and 0.220 respectively), while depolarizing noise imposes the most stringent detection efficiency requirements, exceeding 97\% at 20\% noise where amplitude damping requires 76\%. Security is lost while substantial entanglement remains ($C \approx 0.67$--$0.74$), demonstrating that steering violation, not merely entanglement, determines 1SDI-QKD security. Integrating the BBPSSW purification protocol shows that it functions primarily as a range-extension mechanism: five rounds extend dephasing-limited operation from 10~km to 36~km at 90\% detection efficiency. Accounting for both the $2^n$ pair cost and the cumulative success probability, the effective rate peaks at $ 10^{-3}$ bits per initial pair for dephasing but only $ 10^{-6}$ for amplitude damping and depolarizing noise, identifying phase noise limited links as the regime where purification is worthwhile.

arXiv:2602.00916 [quant-ph]

(or arXiv:2602.00916v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.00916 Focus to learn more arXiv-issued DOI via DataCite

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