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arXiv:2602.00916 · Advanced Quantum Technologies

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

Syed M Arslan, Muhammad T Rahim, Asad Ali, Hashir Kuniyil, Saif Al Kuwari

quant-phSubmitted Jan 31, 2026• Announced Feb 3, 2026• 0 citations• Revised Sep 24, 2026 (v2)
v1 · Jan 31, 2026v2 · Sep 24, 2026
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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.

AI Summary

The paper studies how channel noise changes detection-efficiency requirements and asymptotic key rates in two-setting, one-sided device-independent QKD, and whether entanglement purification can recover positive rates. It considers amplitude damping, phase-flip dephasing, and depolarization acting on one half of an initially entangled two-qubit state, with trusted Pauli measurements at Alice and inefficient, untrusted detection at Bob. Measurement statistics are calculated from the channel models. The Devetak–Winter rate is evaluated using Brown–Fawzi–Fawzi conditional-entropy bounds with a level-1 NPA relaxation incorporating Alice’s measurement anticommutation. The reported noiseless efficiency threshold is $50.1\%$. At ideal detection, positive-rate thresholds are approximately $p=0.50$ for dephasing, $\gamma=0.449$ for amplitude damping, and $q=0.220$ for depolarization, with stated noise-resolution uncertainty around $\pm0.01$. At noise parameter $0.2$, required efficiencies are approximately $85\%$, $76\%$, and $97.5\%$, respectively. Concurrence remains about $0.74$ and $0.67$ at the amplitude-damping and depolarizing rate thresholds. A purification analysis uses Werner-state projection and the BBPSSW fidelity recurrence, accounting for pair consumption and success probabilities. Under the chosen distance-dependent noise models, five rounds extend dephasing-limited positive-rate operation from $10.4$ to $36.3$ km at $\eta_B=0.9$. Reported effective rates reach roughly $10^{-3}$ bits per initial pair for dephasing versus $10^{-6}$ for the other channels. The analysis is asymptotic and numerical, treats noise mechanisms separately, and assumes trusted purification hardware upstream of untrusted detection. Finite-key analysis, experimental validation, alternative purification schemes, and device-independent certification of purification are left for future work.

Likely largely AI-generatedIncrementalOverclaimsStrong assumptionsPossible error

Central claim may not hold: The printed entropy optimization admits Z_a=-I for both Alice outcomes and therefore yields a negative entropy lower bound independently of the data, so it cannot reproduce the positive key rates on which the central numerical claims depend. The reported zero crossings establish failure of a particular achievable-rate certification rather than impossibility of secure key generation, and the claimed necessity of the displayed linear steering witness contradicts the paper's own positive-rate results beyond its witness thresholds. For the specified amplitude-damped Bell state at ideal detection, the reconciliation entropy is h2(gamma)/2 and increases through the reported threshold region, contrary to the explanation used to interpret the amplitude-damping results. The retained-round protocol publicly postselects on Bob's detection flag, but the displayed unconditional entropy calculation is not connected by a security derivation to that postselected key. The quoted metropolitan ranges are conditional predictions from selected decoherence lengths and ideal purification assumptions, not established operational optical-link ranges with an explicit transmission-loss budget.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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•Jul 5, 2021•1 citation
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 (pcrit≈0.50p_{\text{crit}} \approx 0.50pcrit​≈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≈0.67C \approx 0.67C≈0.67--0.740.740.74), 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 10km to 36km at 90% detection efficiency. Accounting for both the 2n2^n2n pair cost and the cumulative success probability, the effective rate peaks at 10−3 10^{-3}10−3 bits per initial pair for dephasing but only 10−6 10^{-6}10−6 for amplitude damping and depolarizing noise, identifying phase noise limited links as the regime where purification is worthwhile.
The paper studies how channel noise changes detection-efficiency requirements and asymptotic key rates in two-setting, one-sided device-independent QKD, and whether entanglement purification can recover positive rates. It considers amplitude damping, phase-flip dephasing, and depolarization acting on one half of an initially entangled two-qubit state, with trusted Pauli measurements at Alice and inefficient, untrusted detection at Bob.
Measurement statistics are calculated from the channel models. The Devetak–Winter rate is evaluated using Brown–Fawzi–Fawzi conditional-entropy bounds with a level-1 NPA relaxation incorporating Alice’s measurement anticommutation. The reported noiseless efficiency threshold is 50.1%50.1\%50.1%. At ideal detection, positive-rate thresholds are approximately p=0.50p=0.50p=0.50 for dephasing, γ=0.449\gamma=0.449γ=0.449 for amplitude damping, and q=0.220q=0.220q=0.220 for depolarization, with stated noise-resolution uncertainty around ±0.01\pm0.01±0.01. At noise parameter 0.20.20.2, required efficiencies are approximately 85%85\%85%, 76%76\%76%, and 97.5%97.5\%97.5%, respectively. Concurrence remains about 0.740.740.74 and 0.670.670.67 at the amplitude-damping and depolarizing rate thresholds.
A purification analysis uses Werner-state projection and the BBPSSW fidelity recurrence, accounting for pair consumption and success probabilities. Under the chosen distance-dependent noise models, five rounds extend dephasing-limited positive-rate operation from 10.410.410.4 to 36.336.336.3 km at ηB=0.9\eta_B=0.9ηB​=0.9. Reported effective rates reach roughly 10−310^{-3}10−3 bits per initial pair for dephasing versus 10−610^{-6}10−6 for the other channels.
The analysis is asymptotic and numerical, treats noise mechanisms separately, and assumes trusted purification hardware upstream of untrusted detection. Finite-key analysis, experimental validation, alternative purification schemes, and device-independent certification of purification are left for future work.
Quantum key distribution (QKD) brings the promise of communication with information-theoretic security but is limited in practice due to its susceptibility to noise, losses, and device imperfections. To address these challenges, we propose a robust high-dimensional (HD) one-sided device-independent QKD (1sDI-QKD) protocol and present a proof-of-principle experimental implementation using photons entangled in the transverse-spatial degree-of-freedom. We develop a systematic security analysis of HD 1sDI-QKD protocols, leveraging quantum steering to certify security, and evaluate achievable secret key rates for different measurement configurations and system dimensions using reverse reconciliation. Our analysis shows that increasing the dimension enhances robustness against both noise and loss. We then demonstrate the key experimental building blocks required for implementing the protocol: (a) a high-quality source of high-dimensional photonic entanglement, and (b) a fully programmable, high-dimensional multi-outcome measurement device operating in up to dimension 11. Using these components, we obtain positive key rates for all investigated dimensions under the fair-sampling assumption, with the highest key rates achieved for dimension d=7. Finally, we discuss the steps required for a practical, loophole-free implementation of 1sDI-QKD in realistic regimes of loss and noise.
Transmitter-side device dependence is a longstanding yet implicit problem in quantum key distribution (QKD), in contrast to the thoroughly addressed measurement-side case. Quantum steering, which intrinsically distinguishes the roles of sender and receiver in entanglement certification, offers a natural route to lifting trust assumptions on the transmitter. Existing one-sided device-independent (1sDI) protocols that exploit quantum steering as the security resource typically operate in a tripartite architecture, whereas adapting them to a transmitter-receiver architecture can introduce a signaling loophole. Here we conceptually formalize the transmitter-device-independence on the basis of faithful quantum steering and propose a practical transmitter-device-independent (TDI) QKD protocol within the 1sDI trust model. The TDI scheme operationalizes the implicit no-signaling condition by enforcing a causal isolation between the input information and the transmitted quantum states, thereby eliminating the associated transmitter-side device vulnerabilities. In a proof-of-principle experiment, we validate the feasibility of the TDI protocol, achieving a key rate in the asymptotic limit of 410~bps over 27~km spool fiber. By delivering TDI security while retaining strong loss tolerance, our approach helps bridge the gap between security and practicality for real-world QKD deployments.
Quantum Key Distribution (QKD) allows spatially separated parties to establish a secret key among themselves based on quantum principles. While QKD systems are being deployed worldwide, their reliance on trusted measurements makes them vulnerable. Moreover, existing protocols have largely focussed on the qubit cases, and rely on the maximally entangled state, a costly resource to generate. Here, we consider the one-sided-device-independent (1SDI) QKD protocols, where one of the measurement devices is trusted while the other is untrusted. The resource in this scenario is quantum steering, an asymmetric form of quantum nonlocality. This is inspired by a real-world scenario, where the trusted party can be considered to be a bank, or any large organisation that has sufficient resources to protect its systems and validate them, while the users are vulnerable to attacks. We then demonstrate that a secure key can be obtained using any pure bipartite entangled state in this setup. Considering realistic detectors and sources based on current technology, we demonstrate that even states that are almost separable can be used to extract a secure key. Moreover, for every pure entangled bipartite state, we find the critical detection efficiencies and visibility to obtain a secure key.
Abstract Quantum key distribution (QKD) is a technique enabling provable secure communication but faces challenges in device characterisation, posing potential security risks. Device-independent (DI) QKD protocols overcome this issue by making minimal device assumptions but are limited in distance because they require high detection efficiencies, which refer to the ability of the experimental setup to detect quantum states. It is thus desirable to find QKD protocols that are based on realistic assumptions on the devices as well as implementable over long distances. In this work, we consider a one-sided DI QKD scheme with two measurements per party and show that it is secure against coherent attacks up to detection efficiencies greater than 50.1% specifically on the untrusted side. This is almost the theoretical limit achievable for protocols with two untrusted measurements. Interestingly, we also show that, by placing the source of states close to the untrusted side, our protocol is secure over distances comparable to standard QKD protocols.
The defining feature of one-sided device-independent quantum key distribution is its asymmetric trust model in which only one party is characterized. This scenario sets an interesting middle ground between high key rates achievable by characterizing devices and the security of full device-independence. Here, we provide new tools, methods, and benchmarks for calculating key rates in this setting. To achieve this, we develop and compare two extensions of the NPA hierarchy and derive finite-size security bounds against general attacks with arbitrary device memory. The latter is based on the Generalized Entropy Accumulation Theorem. We then investigate the performance of various protocols: the BB84 protocol both with and without losses, a qutrit mutually unbiased bases protocol, and protocols based on Bell inequalties such as CHSH and I3322I_{3322}I3322​. We find that the choice of which party is characterized can strongly affects the key rate, surprisingly without a universal ordering. Our work thus offers a general toolbox for calculating key rates for one-sided device-independent QKD protocols.
Quantum key distribution(QKD) is an important area in quantum information theory. There are two kinds of QKD protocols, one is so-called prepare-measure protocols and the other is entanglement-based protocols. For long-distance communications in a noisy environment, entangled-based protocols might be more reliable since they could be supplied by distilled procedures which protect them from noises. In this paper, entanglement-based QKD over certain noisy channels are discussed. We give schemes against collective noises, including collective dephasing(CD) and collective rotation(CR), Pauli noises, amplitude damping(AD) noises, phase damping(PD) noises and mixtures of them. Our discussions are in a direction about how to implement a QKD protocol over noisy channels as in a noiseless channels with no errors, in theoretical. Also, we analyse the efficiency of our schemes, demonstrating that they could be more efficient than the standard entanglement-based QKD scheme.