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Journal of Physics B Atomic Molecular and Optical Physics

Finite-key analysis for high-dimensional quantum key distribution with intensity fluctuations

Ya-Hui Gan, Yang Wang, Wan‐Su Bao, Chun Hua Zhou, Mu-Sheng Jiang, Hong-Wei Li

Published Nov 12, 2018• 4 citations
Publisher

Abstract

Abstract High-dimensional quantum key distribution (HD-QKD) can increase photon information efficiency and be robust to noise. Several HD-QKD experiments have been demonstrated to verify the above appealing features. However, device imperfections, which have great impacts on the security of HD-QKD system, have not been widely discussed. In this paper, we mainly investigate the finite-key analysis against coherent attacks for HD-QKD without and with intensity fluctuations. For the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound and the improved Chernoff bound. When considering the case with intensity fluctuations, we present the finite-key analysis based on Azuma’s inequality. By numerical simulations, we find that the performance of HD-QKD for the finite-key scenario based on the improved Chernoff bound is tighter than those based on the Chernoff bound or Hoeffding’s inequality in terms of the secret-key rate and the maximum transmission distance. Moreover, we find that intensity fluctuations affect the performance of HD-QKD greatly and the effect for short running time of transmission is more obvious.

DOI
10.1088/1361-6455/aaf015

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Abstract High-dimensional quantum key distribution (HD-QKD) can increase photon information efficiency and be robust to noise. Several HD-QKD experiments have been demonstrated to verify the above appealing features. However, device imperfections, which have great impacts on the security of HD-QKD system, have not been widely discussed. In this paper, we mainly investigate the finite-key analysis against coherent attacks for HD-QKD without and with intensity fluctuations. For the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound and the improved Chernoff bound. When considering the case with intensity fluctuations, we present the finite-key analysis based on Azuma’s inequality. By numerical simulations, we find that the performance of HD-QKD for the finite-key scenario based on the improved Chernoff bound is tighter than those based on the Chernoff bound or Hoeffding’s inequality in terms of the secret-key rate and the maximum transmission distance. Moreover, we find that intensity fluctuations affect the performance of HD-QKD greatly and the effect for short running time of transmission is more obvious.
High-dimensional quantum key distribution (HD-QKD) can higher the secret-key capacity and tolerate more errors. Several HD-QKD experiments have been demonstrated over deployed fibers to show promising future toward high-dimensional quantum communication networks. However, the practical security of HD-QKD systems should be widely considered before large-scale application of HD-QKD systems. In this paper, we focus on the HD-QKD based on the dispersive optics (DO-QKD) with both statistical and intensity fluctuations. For the condition only with statistical fluctuations, we present the parameter estimation based on an improved Chernoff bound. When considering the condition with both statistical and intensity fluctuations, we present the parameter estimation based on Azuma’s inequality. By numerical simulations, we find that the parameter estimation for DO-QKD based on the improved Chernoff bound is tighter than the previous work in terms of the secret-key capacity and the maximum transmission distance. Moreover, we find that intensity fluctuations affect the performance of DO-QKD greatly and the effect on smaller data size is more obvious.
High-dimensional quantum states key distribution (HD-QKD) can enable more than one bit per photon and tolerate more noise. Recently, a practical HD-QKD system based on time-phase states has provided a secret key at Mbps over metropolitan distances. For the purposes of further improving the secret key rate of a practical HD-QKD system, we make two main contributions in this work. Firstly, we present an improved parameter estimation for this system in the finite-key scenario based on the Chernoff bound and the improved Chernoff bound. Secondly, we analyze how the dimension d affects the performance of the practical HD-QKD system. We present numerical simulations about the secret key rate of the practical HD-QKD system based on different parameter estimation methods. It is found that using the improved Chernoff bound can improve the secret key rate and maximum channel loss of the practical HD-QKD system. In addition, a mixture of the 4-level and 8-level practical HD-QKD system can provide better performance in terms of the key generation rate over metropolitan distances .
The decoy-state quantum key distribution (QKD) protocol has been widely used in commercial QKD systems. Several QKD field networks show its practicability and commercial prospects. Importantly, practical decoy-state QKD systems should be characterized with device imperfections. In this paper, for the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound for a practical decoy-state QKD protocol and compare performances of that based on Hoeffding's inequality and the Chernoff bound, respectively. Taking intensity fluctuations into consideration, we present the finite-key analysis with composable security against general attacks based on Azuma's inequality. Our numerical results show that the finite-key analysis based on the Chernoff bound is tighter than Hoeffding's inequality when the total number of transmitting signals $N<1\ifmmode\times\else\texttimes\fi{}{10}^{12}$. Moreover, the intensity fluctuations' influence is more obvious when the data size of total transmitting signals is small. Our results emphasize the importance of the stability of the intensity modulator as well as the accurate estimation of emitted pulse's intensity.
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.
Quantum key distribution (QKD) has attracted much attention due to its unconditional security. High-dimensional quantum key distribution (HD-QKD) is a brand-new type of QKD protocol that has many excellent advantages. Nonetheless, practical imperfections in realistic devices that are not considered in the theoretical security proof may have an impact on the practical security of realistic HD-QKD systems. In this paper, we research the influence of a realistic intensity modulator on the practical security of HD-QKD systems with the decoy-state method and finite-key effects. We demonstrate that there is a certain impact in the secret key rate and the transmission distance when taking practical factors into security analysis.
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.