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Physical Review A

Finite-key analysis for one-sided device-independent quantum key distribution

Yang Wang, Wan‐Su Bao, Hong-Wei Li, Chun Hua Zhou, Yuan Li

Published Nov 20, 2013• 34 citations
Publisher

Abstract

Compared with device-independent quantum key distribution (DI-QKD), one-sided DI-QKD (1sDI-QKD) requires lower detector efficiencies and provides a better opportunity for experimental implementation. Based on the asymptotic analysis of 1sDI-QKD, we analyze the security of 1sDI-QKD with finite resources by using the uncertainty relation for smooth entropies. By numerical simulation we obtain the minimal number of the exchanged quantum signals initially shared by Alice and Bob for different detection efficiencies. The results indicate that finite resources should not be neglected in practical implementation of 1sDI-QKD.

DOI
10.1103/physreva.88.052322

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Compared with device-independent quantum key distribution (DI-QKD), one-sided DI-QKD (1sDI-QKD) requires lower detector efficiencies and provides a better opportunity for experimental implementation. Based on the asymptotic analysis of 1sDI-QKD, we analyze the security of 1sDI-QKD with finite resources by using the uncertainty relation for smooth entropies. By numerical simulation we obtain the minimal number of the exchanged quantum signals initially shared by Alice and Bob for different detection efficiencies. The results indicate that finite resources should not be neglected in practical implementation of 1sDI-QKD.
Compared with full device-independent quantum key distribution (DI-QKD), one-side device-independent QKD (1sDI-QKD) needs fewer requirements, which is much easier to meet. In this paper, by applying recently developed novel time–energy entropic uncertainty relations, we present a time–energy high-dimensional one-side device-independent quantum key distribution (HD-QKD) and provide the security proof against coherent attacks. Besides, we connect the security with the quantum steering. By numerical simulation, we obtain the secret key rate for Alice’s different detection efficiencies. The results show that our protocol can performance much better than the original 1sDI-QKD. Furthermore, we clarify the relation among the secret key rate, Alice’s detection efficiency, and the dispersion coefficient. Finally, we simply analyze its performance in the optical fiber channel.
The length of signal pulses is finite in practical quantum key distribution. The finite-key analysis of an unconditional quantum key distribution is a burning problem, and the efficient quantum key distribution protocol suitable for practical implementation, measurement-device-independent quantum key distribution (MDI QKD), was proposed very recently. We give the finite-key analysis of MDI QKD, which removes all detector side channels and generates many orders of key rate higher than that of full-device-independent quantum key distribution. The secure bound of the ultimate key rate is obtained under the statistical fluctuations of relative frequency, which can be applied directly to practical threshold detectors with low detection efficiency and highly lossy channels. The bound is evaluated for reasonable values of the observed parameters. The simulation shows that the secure distance is around 10 km when the number of sifted data is 1010{10}^{10}1010. Moreover the secure distance would be much longer in practice because of some simplified treatments used in our paper.
We analyze the security and feasibility of a protocol for quantum key distribution (QKD) in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and device-independent QKD (DI-QKD), where neither do, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.
We analyze the security and feasibility of a protocol for Quantum Key Distribution (QKD), in a context where only one of the two parties trusts his measurement apparatus. This scenario lies naturally between standard QKD, where both parties trust their measurement apparatuses, and Device-Independent QKD (DI-QKD), where neither does, and can be a natural assumption in some practical situations. We show that the requirements for obtaining secure keys are much easier to meet than for DI-QKD, which opens promising experimental opportunities. We clarify the link between the security of this one-sided DI-QKD scenario and the demonstration of quantum steering, in analogy to the link between DI-QKD and the violation of Bell inequalities.
One of the most pressing issues in quantum key distribution (QKD) is the problem of detector side-channel attacks. To overcome this problem, researchers proposed an elegant “time-reversal” QKD protocol called measurement-device-independent QKD (MDI-QKD), which is based on time-reversed entanglement swapping. However, MDI-QKD is more challenging to implement than standard point-to-point QKD. Recently, an intermediary QKD protocol called detector-device-independent QKD (DDI-QKD) has been proposed to overcome the drawbacks of MDI-QKD, with the hope that it would eventually lead to a more efficient detector side-channel-free QKD system. Here, we analyze the security of DDI-QKD and elucidate its security assumptions. We find that DDI-QKD is not equivalent to MDI-QKD, but its security can be demonstrated with reasonable assumptions. On the more practical side, we consider the feasibility of DDI-QKD and present a fast experimental demonstration (clocked at 625 MHz), capable of secret key exchange up to more than 90 km.
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 10~km to 36~km at 90\% detection efficiency. Accounting for both the 2n2^n2n 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.