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Scientific Reports

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources

Tingting Song, Su‐Juan Qin, Qiaoyan Wen, Yukun Wang, Heng-Yue Jia

Published Oct 16, 2015• 14 citations
Publisher

Abstract

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

DOI
10.1038/srep15276

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In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.
Passive decoy-state quantum key distribution (QKD) systems, proven to be more desirable than the active ones in some scenarios, also have the problem of device imperfections like intensity fluctuations. In this paper, the formula of key generation rate of the passive decoy-state protocol using the weak coherent pulse (WCP) source with intensity fluctuation is given, and then the influence of intensity fluctuations on the performance of the passive decoy-state protocol is rigorously characterized. From numerical simulations, it can be seen that intensity fluctuations have non-negligible influence on the performance of the passive decoy-state QKD protocol with WCP source. Most importantly, our simulations show that, under the same deviation of intensity fluctuations, the passive decoy-state method performs better than the active one decoy-state method and is close to the active vacuum + weak decoy-state method.
For quantum key distribution (QKD) using spontaneous parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol has been proved to be efficiently close to the theoretical limit of an infinite decoy-state protocol. In this paper, we apply a tight finite-key analysis for the passive decoy-state QKD using SPDCSs. Combining the security bound based on the uncertainty principle with the passive decoy-state protocol, a concise and stringent formula for calculating the key generation rate for QKD using SPDCSs is presented. The simulation shows that the secure distance under our formula can reach up to 182 km when the number of sifted data is 1010{10}^{10}1010. Our results also indicate that, under the same deviation of statistical fluctuation due to finite-size effects, the passive decoy-state QKD with SPDCSs can perform as well as the active decoy-state QKD with a weak coherent source.
The fully passive source is capable of passively generating decoy states and performing passive encoding simultaneously, avoiding the side-channel risks caused by active modulation operations at the source end, thus effectively enhance the security in quantum key distribution (QKD). Existing fully passive QKD protocol and experiments exploit phase-randomized coherent pulses. In this paper, we propose a fully passive QKD protocol using parametric down-conversion source. The decoy state generation and encoding operation can be carried out passively by parameter down-conversion progress. This protocol has several advantages. First, it can also eliminate all side channels in active modulators. Second, compared with fully passive QKD protocol with phase-randomized coherent pulses, our protocol can significantly increase the key rate and extend the communication distance. Meanwhile, in terms of the transmission rate, our protocol is also closer to that of actively modulated QKD and can achieve fully passive modulation with fewer resources. Moreover, combined with measurement-device-independent (MDI) QKD, this protocol can even potentially achieve robustness against side channels in both detectors and modulators.
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.
Passive decoy-state quantum key distribution systems, proven to be more desirable than active ones in some scenarios, also have the problem of device imperfections like finite-length keys. In this paper, based on the WCP source which can be used for the passive decoy-state method, we obtain the expressions of single-photon error rates, single-photon counts, and phase error rates. According to the information of smooth min-entropy, we calculate the key generation rate under the condition of finite-length key. Key generation rates with different numbers of pulses are compared by numerical simulations. From the results, it can be seen that the passive decoy-state method can have good results if the total number of pulses reaches 10 10 . We also simulate the passive decoy-state method with different probabilities of choosing a pulse for parameter estimation when the number of pulses is fixed.
The performance of active decoy-state quantum key distribution (QKD) system with an untrusted source is compared with that of passive decoy-state QKD. The key generation rate with the change of the secure transmission distance is shown under the condition of active decoy-state (or passive decoy-state) QKD where we pick the data size to be N=1012. The security characteristics of the passive scheme are studied with statistical fluctuation of the counting rate and the intensity of the practical source. At communication wavelength 1310 nm or 1550 nm, The security range of communication distance is [73.2 km, 96.5 km] or [104.5 km, 137.9 km] respectively. This analysis will provide important theoretical parameters for practical QKD experiment.