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Chinese Physics Letters

Finite-Key Analysis for a Practical High-Dimensional Quantum Key Distribution System Based on Time-Phase States

Ya-Hui Gan, Yang Wang, Wan‐Su Bao, Ru-Shi He, Chun Hua Zhou, Mu-Sheng Jiang

Published Apr 1, 2019• 7 citations
Publisher

Abstract

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 .

DOI
10.1088/0256-307x/36/4/040301

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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 .
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.
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.
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.
High-dimensional quantum key distribution (HD-QKD) allows two parties to generate multiple secure bits of information per detected photon. In this work, we show that decoy-state protocols can be practically implemented for HD-QKD using only one or two decoy states. HD-QKD with two decoy states, under realistic experimental constraints, can generate multiple secure bits per coincidence at distances over 200 km and at rates similar to those achieved by a protocol with infinite decoy states. Furthermore, HD-QKD with only one decoy state is practical at short distances, where it is almost as secure as a protocol with two decoy states. HD-QKD with only one or two decoy states can therefore be implemented to optimize the rate of secure quantum communications.
Higher Dimensional Quantum Key Distribution (HD-QKD) improves information capacity and security compared to binary QKD systems. Previous HD-QKD implementations have required d+1 (d refers to encoding dimension) single-photon detectors, limiting large-scale implementation. In contrast, another HD-QKD implementation using coherent one-way (COW) protocol hardware with two detectors achieved a secret key rate (SKR) of 155 kbps for an 8-D system and 2.7% QBER tolerance for a 16-D system with qubit scrambling across a time window. In this paper, we theoretically simulate and experimentally demonstrate time-bin encoded HD-QKD using COW protocol hardware with two single-photon detectors operating at standard telecom wavelengths, achieving a remarkable maximum encoding of 6 bits per photon (i.e., 56-d system). Our HD-QKD system incorporates a practical decoy-state technique to counter the photon number splitting attack, allowing greater flexibility in choosing higher mean photon number thereby achieving higher SKR and distances. This implementation demonstrates a remarkable ninefold increase in SKR for a 16-d system (210 kbps over 25 km of standard single-mode fiber) compared to qubit-based systems, with a QBER tolerance of 13.5% for d = 16. Notably, we achieved positive key rates for emulated loss up to 131 km of fiber length for d = 8. By optimizing detector deadtime and mean photon number using our theoretical model, we achieve enhanced key rates and security. Our findings highlight the superiority of our approach and lay the foundation for high throughput HD-QKD implementation, offering a secure and efficient method for transmitting sensitive information.