Decoy-state Measurement-device-independent Quantum Key Distribution Research Articles

Advantages of Asynchronous Measurement-Device-Independent Quantum Key Distribution in Intercity Networks

The new variant of measurement-device-independent quantum key distribution (MDI-QKD), called asynchronous MDI-QKD or mode-pairing MDI-QKD, offers similar repeater-like rate-loss scaling but has the advantage of simple technology implementation by exploiting an innovative post-measurement pairing technique. We herein present an evaluation of the practical aspects of decoy-state asynchronous MDI-QKD. To determine its effectiveness, we analyze the optimal method of decoy-state calculation and examine the impact of asymmetrical channels and multi-user networks. Our simulations show that, under realistic conditions, aynchronous MDI-QKD can furnish the highest key rate with MDI security as compared to other QKD protocols over distances ranging from 50 km to 480 km. At fiber distances of 50 km and 100 km, the key rates attain 6.02 Mbps and 2.29 Mbps respectively, which are sufficient to facilitate real-time one-time-pad video encryption. Our findings indicate that experimental implementation of asynchronous MDI-QKD in intercity networks can be both practical and efficient.

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing.

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user’s pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method.

Measurement-device-independent quantum key distribution with leaky sources

Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detection side-channels from quantum communication systems. The security proofs require, however, that certain assumptions on the sources are satisfied. This includes, for instance, the requirement that there is no information leakage from the transmitters of the senders, which unfortunately is very difficult to guarantee in practice. In this paper we relax this unrealistic assumption by presenting a general formalism to prove the security of MDI-QKD with leaky sources. With this formalism, we analyze the finite-key security of two prominent MDI-QKD schemes—a symmetric three-intensity decoy-state MDI-QKD protocol and a four-intensity decoy-state MDI-QKD protocol—and determine their robustness against information leakage from both the intensity modulator and the phase modulator of the transmitters. Our work shows that MDI-QKD is feasible within a reasonable time frame of signal transmission given that the sources are sufficiently isolated. Thus, it provides an essential reference for experimentalists to ensure the security of implementations of MDI-QKD in the presence of information leakage.

Laser-seeding Attack in Quantum Key Distribution

Quantum key distribution (QKD) based on the laws of quantum physics allows the secure distribution of secret keys over an insecure channel. Unfortunately, imperfect implementations of QKD compromise its information-theoretical security. Measurement-device-independent quantum key distribution (MDI-QKD) is a promising approach to remove all side channels from the measurement unit, which is regarded as the "Achilles' heel" of QKD. An essential assumption in MDI-QKD is however that the sources are trusted. Here we experimentally demonstrate that a practical source based on a semiconductor laser diode is vulnerable to a laser seeding attack, in which light injected from the communication line into the laser results in an increase of the intensities of the prepared states. The unnoticed increase of intensity may compromise the security of QKD, as we show theoretically for the prepare-and-measure decoy-state BB84 and MDI-QKD protocols. Our theoretical security analysis is general and can be applied to any vulnerability that increases the intensity of the emitted pulses. Moreover, a laser seeding attack might be launched as well against decoy-state based quantum cryptographic protocols beyond QKD.

Versatile security analysis of measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) is the only known QKD scheme that can completely overcome the problem of detection side-channel attacks. Yet, despite its practical importance, there is no standard approach towards proving the security of MDI-QKD. Here, we present a simple numerical method that can efficiently compute almost-tight security bounds for any discretely modulated MDI-QKD protocol. To demonstrate the broad utility of our method, we use it to analyze the security of coherent-state MDI-QKD, decoy-state MDI-QKD with leaky sources, and a variant of twin-field QKD called phase-matching QKD. In all of the numerical simulations (using realistic detection models) we find that our method gives significantly higher secret key rates than those obtained with current security proof techniques. Interestingly, we also find that phase-matching QKD using only two coherent test states is enough to overcome the fundamental rate-distance limit of QKD. Taken together, these findings suggest that our security proof method enables a versatile, fast, and possibly optimal approach towards the security validation of practical MDI-QKD systems.

Finite-key analysis of practical decoy-state measurement-device-independent quantum key distribution with unstable sources

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.

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) is a promising protocol for realizing long-distance secret keys sharing. However, its key rate is relatively low when the finite-size effect is taken into account. In this paper, we consider statistical fluctuation analysis for the three-intensity decoy-state MDI-QKD system based on the recent work (Zhang et al. in Phys Rev A 95:012333, 2017) and further compare its performance with that of applying the Gaussian approximation technique and the Chernoff bound method. The numerical simulations demonstrate that the new method has apparent enhancement both in key generation rate and transmission distance than using Chernoff bound method. Meanwhile, the present work still shows much higher security than Gaussian approximation analysis.

Improving the Performance of Practical Decoy-State Measurement-Device-Independent Quantum Key Distribution with Biased Basis Choice**Supported by the National Key Research and Development Program of China under Grant Nos. 2018YFA0306400, 2017YFA0304100, the National Natural Science Foundation of China under Grants Nos. 61475197, 61590932, 11774180, 61705110, the Natural Science Foundation of the Jiangsu Higher Education Institutions under Grant Nos. 15KJA120002, 17KJB140016, the Outstanding

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.

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with four-intensity decoy-state method.

Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation analysis.

Fluctuations of Internal Transmittance in Security of Measurement-Device-Independent Quantum Key Distribution with an Untrusted Source**Supported by the National Basic Research Program of China under Grant No. 2013CB338002 and the National Natural Science Foundation of China under Grant Nos. 61505261, 61675235, 61605248, 11304397

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to detector side channel attacks, which is a crucial security loophole problem in traditional QKD. In order to relax a key assumption that the sources are trusted in MDI-QKD, an MDI-QKD protocol with an untrusted source has been proposed. For the security of MDI-QKD with an untrusted source, imperfections in the practical experiment should also be taken into account. In this paper, we analyze the effects of fluctuations of internal transmittance on the security of a decoy-state MDI-QKD protocol with an untrusted source. Our numerical results show that both the secret key rate and the maximum secure transmission distance decrease when taken fluctuations of internal transmittance into consideration. Especially, they are more sensitive when Charlie’s mean photon number per pulse is smaller. Our results emphasize that the stability of correlative optical devices is important for practical implementations.

Making the decoy-state measurement-device-independent quantum key distribution practically useful

The relatively low key rate seems to be the major barrier to its practical use for the decoy state measurement device independent quantum key distribution (MDIQKD). We present a 4-intensity protocol for the decoy-state MDIQKD that hugely raises the key rate, especially in the case the total data size is not large. Also, calculation shows that our method makes it possible for secure private communication with {\em fresh} keys generated from MDIQKD with a delay time of only a few seconds.

Decoy-state measurement-device-independent quantum key distribution with mismatched-basis statistics

Measurement-device-independent quantum key distribution (MDI-QKD) is aimed at removing all detector side channel attacks, while its security relies on the assumption that the encoding systems including sources are fully characterized by the two legitimate parties. By exploiting the mismatched-basis statistics in the security analysis, MDI-QKD even with uncharacterized qubits can generate secret keys. In this paper, considering the finite size effect, we study the decoy-state MDI-QKD protocol with mismatched-basis events statistics by performing full parameter optimization, and the simulation result shows that this scheme is very practical.

Analysis of measurement-device-independent quantum key distribution under asymmetric channel transmittance efficiency

Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks. Based on decoy-state method, MDI-QKD can be implemented with nonperfect single-photon sources. In this paper, the performance of three-intensity decoy-state MDI-QKD under asymmetric channel transmittance efficiency is considered and compared with the results under the symmetric choice scenario. The relation between security key generation rate and the total transmission loss is shown with exchanged ratio of the two distances between Alice to the untrusted third party and Bob to the third party. Based on the relationship, an optimal intensity method is proposed to improve the key rate for a fixed distance ratio, which will provide important parameters for practical experiment.

Measurement-device-independent quantum key distribution with odd coherent state

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 rate can be obtained by estimating the gain and quantum bit error rate for various input photon numbers. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy-state MDI-QKD with OCS and obtain a practical key rate.

Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field-tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual performance of former demonstrations. Here, we present analytical and numerical decoy-state methods with one, two and three decoy states. We provide a clear comparison among these methods and find that two decoy states already enable a near optimal estimation and more decoy states cannot improve the key rate much in either asymptotic or finite-data settings. Furthermore, we perform a full optimization of system parameters and show that full optimization can significantly improve the key rate in the finite-data setting. By simulating a real experiment, we find that full optimization can increase the key rate by more than one order of magnitude compared to non-optimization. A local search method to optimize efficiently the system parameters is proposed. This method can be four orders of magnitude faster than a trivial exhaustive search to achieve a similar optimal key rate. We expect that this local search method could be valuable for general fields in physics.

Measurement-device-independent quantum key distribution with odd coherent state

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 safe. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy state MDI-QKD with OCS and obtain a practical key rate.

Practical decoy-state measurement-device-independent quantum key distribution

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.