High-dimensional quantum resources provide the ability to encode several bits of information on a single photon, which can particularly increase the secret key rate rate of quantum key distribution (QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations. Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.
High-dimensional quantum resources provide the ability to encode several bits of information on a single photon, which can particularly increase the secret key rate rate of quantum key distribution (QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations. Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.
High-dimensional quantum key distribution (QKD) allows achievement of information-theoretic secure communications, providing high key-generation rates, which cannot, in principle, be obtained by QKD protocols with binary encoding. Nonetheless, the amount of experimental resources needed increases as the quantum states to be detected belong to a larger Hilbert space, thus raising the costs of practical high-dimensional systems. Here, we present an alternative scheme for fiber-based four-dimensional QKD, with time and phase encoding and one-decoy state technique. Quantum state transmission is tested over different channel lengths up to 145 km of standard single-mode fiber, evaluating the enhancement of the secret key rate in comparison to the three-state two-dimensional BB84 protocol, which is tested with the same experimental setup. Our scheme allows measurement of the four-dimensional states with a simplified and compact receiver, where only two single-photon detectors are necessary, thus making it a cost-effective solution for practical and fiber-based QKD.
In light of the growing widely utilized single-photon avalanche detectors, dead time is inevitable due to the presence of afterpulse. Dead time is a critical factor that influences the count rate and the secret key rate (SKR) of quantum key distribution (QKD). It is particularly significant in time-bin-encoding systems, while prior models fail to accurately estimate the gains. Of note, it introduces correlations between early bins and late bins, hence bits with strong correlation and security risks. Here, we put forward a realistic model that precisely characterizes the response of detectors for time-bin-encoding systems. Our model not only improves the accuracy of gain predictions, showing an excellent match with the Monte Carlo simulation results, but also provides theoretical support for data processing, helping to mitigate security risks. Finally, leveraging our model, we can get a much higher SKR than prior models and further enhance the performance of practical QKD systems by adjusting the detector parameters. Our simulation results demonstrate that our model is essential for the application and deployment of QKD systems in practice.
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 passive decoy method, a candidate for high-speed quantum key distribution (QKD), can prepare laser pulses with various photon-number distributions according to the responses of the transmitter's detectors, which usually adopts the single-photon avalanche photodiode (SPAD) in QKD. As an intrinsic characteristic of the SPAD, the afterpulse can introduce random detector responses, however, is regrettably ignored in passive schemes. Here we develop an analytical model for passive schemes in the finite-resource regime to describe the afterpulse effect on the detectors of both transmitter and receiver. The photon-number distributions biased by afterpulses are corrected, which reveals that the secure key rate is significantly overrated when the afterpulse is ignored. Moreover, our model can increase the tolerance of passive decoy source to afterpulse effect as the result shows that the secret key rates are comparable at different afterpulse probability by reoptimization.
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.
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.