Measurement-device-independent quantum key distribution (MDI-QKD) can remove all the side-channel attacks from imperfections in the detection side. However, finite-size resources undoubtedly influence its performance and the achievable finite secret key rates of MDI-QKD are typically lower than that of standard decoy-state QKD. In this paper, we introduce the efficient decoy-state method with biased basis choice into the finite-key analysis and propose a decoy-state protocol for MDI-QKD. By applying vacuum + weak decoy-state method, we analytically derive concise formulas for estimating the lower bound of single-photon yield and the upper bound of phase error rate in the case of finite resources. The simulations show that proper basis choice combined with deliberate intensity choice can substantially enhance the performance of decoy-state MDI-QKD and, without a full optimization program, our protocol can bring a long-distance implementation (168 km on standard optical fiber) of MDI-QKD with a reasonable data size of total transmitting signals $(N={10}^{15})$.
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all the side-channel attacks from imperfections in the detection side. However, finite-size resources undoubtedly influence its performance and the achievable finite secret key rates of MDI-QKD are typically lower than that of standard decoy-state QKD. In this paper, we introduce the efficient decoy-state method with biased basis choice into the finite-key analysis and propose a decoy-state protocol for MDI-QKD. By applying vacuum + weak decoy-state method, we analytically derive concise formulas for estimating the lower bound of single-photon yield and the upper bound of phase error rate in the case of finite resources. The simulations show that proper basis choice combined with deliberate intensity choice can substantially enhance the performance of decoy-state MDI-QKD and, without a full optimization program, our protocol can bring a long-distance implementation (168 km on standard optical fiber) of MDI-QKD with a reasonable data size of total transmitting signals (N=1015).
A novel protocol, measurement-device-independent quantum key distribution (MDI-QKD), removes all attacks from the detection system, the most vulnerable part in QKD implementations. In this paper, we present an analysis for practical aspects of MDI-QKD. To evaluate its performance, we study various error sources by developing a general system model. We find that MDI-QKD is highly practical and thus can be easily implemented with standard optical devices. Moreover, we present a simple analytical method with only two (general) decoy states for the finite decoy-state analysis. This method can be used directly by experimentalists to demonstrate MDI-QKD. By combining the system model with the finite decoy-state method, we present a general framework for the optimal choice of the intensities of the signal and decoy states. Furthermore, we consider a common situation, namely asymmetric MDI-QKD, in which the two quantum channels have different transmittances. We investigate its properties and discuss how to optimize its performance. Our work is of interest not only to experiments demonstrating MDI-QKD but also to other non-QKD experiments involving quantum interference.
Abstract Statistical fluctuations are unavoidable in realistic quantum key distribution (QKD) due to finite-size effect. Based on the four-intensity proposal on measurement-device-independent QKD (MDI-QKD) in [Phys. Rev. A 93 (2016) 042324], we particularly analyze the scenario that only three intensities are used, namely a three-intensity decoy-state MDI-QKD with biased basis choice. After performing full parameter optimization method, simulations results demonstrate that this scenario can obtain distinct enhancement compared with the conventional unbiased three-intensity decoy-state method, e.g. Xu et al.’s [Phys. Rev. A 89 (2014) 052333]. Furthermore, results also show that it works more efficiently by using HSPS than using WCS at longer transmission distance.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to detector side channel attacks, which is a notorious security loophole problem in QKD. Importantly, both finite-key effects and intensity fluctuations of the practical photon sources are nonnegligible in a full key rate analysis of practical QKD. In this paper, for the case with finite-key effects and without intensity fluctuations, we present a way to estimate the phase error rate for MDI-QKD and compare performances of the parameter estimation based on Hoeffding’s inequality and the Chernoff bound. By using Azuma’s inequality, we also present the finite-key analysis with composable security against general attacks for a biased decoy-state MDI-QKD protocol with intensity fluctuations. Our simulation results show that the effect of our phase error rate estimation is almost the same as the results in Phys. Rev. A91, 022313 (2015)PLRAAN1050-294710.1103/PhysRevA.91.022313, and the parameter estimation using the Chernoff bound is tighter than that using Hoeffding’s inequality. In addition, the influence of intensity fluctuations is more obvious when the data size of total transmitting signals is small. Our results highlight that it is important to keep the stability of the intensity modulator and estimate accurately the emitted pulse’s intensity for practical implementations.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks; thus when it is combined with the decoy-state method, the final key is unconditionally secure, even if a practical weak coherent source is used by Alice and Bob. However, until now, the analysis of decoy-state MDI-QKD with a weak coherent source is incomplete. In this paper, we derive, with only vacuum+weak decoy state, some tight formulas to estimate the lower bound of yield and the upper bound of error rate for the fraction of signals in which both Alice and Bob send a single-photon pulse to the untrusted third party Charlie. The numerical simulations show that our method with only vacuum+weak decoy state can asymptotically approach the theoretical limit of the infinite number of decoy states. Furthermore, the statistical fluctuation due to the finite length of date is also considered based on the standard statistical analysis.
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detector loopholes. When it is combined with the decoy-state method, the final key is unconditionally secure, even if Alice and Bob do not have strict single-photon sources. However, active modulation of source intensity, which is used to generate the decoy state, may leave side channels and leak additional information to Eve. In this paper, we consider the MDI-QKD with a passive decoy state, in which both Alice and Bob send pulses to an untrusted third party, Charlie. Then, in order to estimate the key generation rate, we derive two tight formulas to estimate the lower bound of the yield and the upper bound of the error rate that both Alice and Bob send a single-photon pulse to Charlie. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the standard statistical analysis.
Measurement-device-independent quantum key distribution (MDI-QKD) with the active decoy state method can remove all detector loopholes, and resist the imperfections of sources. But it may lead to side channel attacks and break the security of QKD system. In this paper, we apply the passive decoy state method to the MDI-QKD based on polarization encoding mode. Not only all attacks on detectors can be removed, but also the side channel attacks on sources can be overcome. We get that the MDI-QKD with our passive decoy state method can have a performance comparable to the protocol with the active decoy state method. To fit for the demand of practical application, we discuss intensity fluctuation in the security analysis of MDI-QKD protocol using passive decoy state method, and derive the key generation rate for our protocol with intensity fluctuation. It shows that intensity fluctuation has an adverse effect on the key generation rate which is non-negligible, especially in the case of small data size of total transmitting signals and long distance transmission. We give specific simulations on the relationship between intensity fluctuation and the key generation rate. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account.