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EPJ Quantum Technology

An intelligent threshold selection method to improve orbital angular momentum-encoded quantum key distribution under turbulence

Jiahao Li, Jie Tang, Xingyu Wang, Yang Xue, Huicun Yu, Zhi-Feng Deng, Yuexiang Cao, Ying Liu, Dan Wu, Haoran Hu, Ya Wang, Huazhi Lun, Jiahua Wei, Bo Zhang, Bo Liu, Lei Shi

Published Jun 6, 2024• 2 citations
Publisher

Abstract

Abstract High-dimensional quantum key distribution (HD-QKD) encoded by orbital angular momentum (OAM) presents significant advantages in terms of information capacity. However, perturbations caused by free-space atmospheric turbulence decrease the performance of the system by introducing random fluctuations in the transmittance of OAM photons. Currently, the theoretical performance analysis of OAM-encoded QKD systems exists a gap when concerning the statistical distribution under the free-space link. In this article, we analyzed the security of QKD systems by combining probability distribution of transmission coefficient (PDTC) of OAM with decoy-state BB84 method. To address the problem that the invalid key rate is calculated in the part transmittance interval of the post-processing process, an intelligent threshold method based on neural network is proposed to improve OAM-encoded QKD, which aims to conserve computing resources and enhance system efficiency. Our findings reveal that the ratio of root mean square (RMS) OAM-beam radius to Fried constant plays a crucial role in ensuring secure key generation. Meanwhile, the training error of neural network is at the magnitude around 10−3, indicating the ability to predict optimization parameters quickly and accurately. Our work contributes to the advancement of parameter optimization and prediction for free-space OAM-encoded HD-QKD systems. Furthermore, it provides valuable theoretical insights to support the development of free-space experimental setups.

DOI
10.1140/epjqt/s40507-024-00251-z

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Abstract High-dimensional quantum key distribution (HD-QKD) encoded by orbital angular momentum (OAM) presents significant advantages in terms of information capacity. However, perturbations caused by free-space atmospheric turbulence decrease the performance of the system by introducing random fluctuations in the transmittance of OAM photons. Currently, the theoretical performance analysis of OAM-encoded QKD systems exists a gap when concerning the statistical distribution under the free-space link. In this article, we analyzed the security of QKD systems by combining probability distribution of transmission coefficient (PDTC) of OAM with decoy-state BB84 method. To address the problem that the invalid key rate is calculated in the part transmittance interval of the post-processing process, an intelligent threshold method based on neural network is proposed to improve OAM-encoded QKD, which aims to conserve computing resources and enhance system efficiency. Our findings reveal that the ratio of root mean square (RMS) OAM-beam radius to Fried constant plays a crucial role in ensuring secure key generation. Meanwhile, the training error of neural network is at the magnitude around 10−3, indicating the ability to predict optimization parameters quickly and accurately. Our work contributes to the advancement of parameter optimization and prediction for free-space OAM-encoded HD-QKD systems. Furthermore, it provides valuable theoretical insights to support the development of free-space experimental setups.
A high-dimensional quantum key distribution (QKD), which adopts degrees of freedom of the orbital angular momentum (OAM) states, is beneficial to realize secure and high-speed QKD. However, the helical phase of a vortex beam that carries OAM is sensitive to the atmospheric turbulence and easily distorted. In this paper, an adaptive compensation method using deep learning technology is developed to improve the performance of OAM-encoded QKD schemes. A convolutional neural network model is first trained to learn the mapping relationship of intensity profiles of inputs and the turbulent phase, and such mapping is used as feedback to control a spatial light modulator to generate a phase screen to correct the distorted vortex beam. Then an OAM-encoded QKD scheme with the capability of real-time phase correction is designed, in which the compensation module only needs to extract the intensity distributions of the Gaussian probe beam and thus ensures that the information encoded on OAM states would not be eavesdropped. The results show that our method can efficiently improve the mode purity of the encoded OAM states and extend the secure distance for the involved QKD protocols in the free-space channel, which is not limited to any specific QKD protocol.
Abstract High-dimensional quantum key distribution (HD-QKD) is a topic of growing interest in the quantum communication community, not only for its inherent properties but also for its possible applications. As the typical freedom in HD-QKD, orbital angular momentum (OAM) has made significant advancements in experiments recently. However, in the airborne scenario, different states suffer different amounts of misalignment and turbulence. A complete theoretical analysis model for the transmission characteristics of OAM in atmospheric channels is lacking. In this paper, we systematically analyze the extent to which degeneration including channel power loss and mode crosstalk are influenced by misalignment and turbulence effects. Furthermore, the performance of OAM-encoded HD-QKD system in different dimensions is evaluated while incorporating finite-key effects. We demonstrate that the performance of OAM-encoded HD-QKD will be better at short range, which provide a reference to implement QKD based on task requirements. Since OAM is desired to increase the capacity of QKD system and experiments have already been carried out, our work can not only bridge the gap between theory and practice, but also optimize experimental parameters and improve system performance.
Quantum key distribution (QKD) technology has demonstrated remarkable practicality and sustained developmental trends in the current field of quantum communication. This paper focuses on a novel and potent quantum communication protocol, specifically quantum key distribution utilizing the encoding of information through orbital angular momentum (OAM) of photons. OAM states, owing to their distinctive properties, exhibit significant advantages in terms of information capacity and channel robustness. However, the sensitivity of OAM states to atmospheric conditions and challenges arising from wavefront distortions necessitate in-depth investigation. Additionally, the unique structure of OAM beams has raised concerns about geometric losses. By analyzing the impact of atmospheric turbulence and geometric losses on the transmission performance when applying the OAM-QKD protocol in free space, this paper explores variations in system losses under different OAM orders. Simulation results indicated that as the channel distance increases, system losses gradually escalate. Furthermore, with an increase in OAM order, although the system's sensitivity to atmospheric turbulence diminishes, geometric losses exhibit an exponential increase. Addressing this issue, our research suggested that when considering free-space quantum key distribution with OAM encoding, selecting an OAM order of 1 for the beam achieves minimal transmission losses. Therefore, in practical applications, employing OAM beams with <?TeX l=1l = 1l=1 ?> emerges as an effective strategy to optimize the performance of the OAM-QKD protocol in free space.
High-dimensional quantum key distribution (HD-QKD) provides notable advantages over qubit-based QKD, including higher key rates and greater noise resilience. Leveraging the orbital angular momentum states of structured photons to encode information has become a prominent method for implementing HD-QKD. However, practical challenges such as state-dependent diffraction, limited receiving aperture, and atmospheric turbulence impose constraints on the attainable performance and encoding dimension of QKD in free-space links. In this work, we address these challenges with focused, structured photons. Numerical simulations indicate that this method markedly enhances transmission efficiency and improves the robustness against turbulence, resulting in higher key rates and extended transmission distances in free-space HD-QKD. Additionally, focused, structured photons allow us to implement higher-dimensional QKD and enable QKD systems to achieve superior performance with smaller receiving apertures in a turbulent free-space link. This makes our approach particularly advantageous for applications of unmanned aerial vehicles and satellite platforms. Our work contributes to exploring the robust QKD schemes employing structured photons and may promote its application in quantum networks.
In this paper, a free-space quantum key distribution (QKD) system based on BB84 protocol is studied assuming that the transmitted quantum bits are multiplexed spatially based on orthogonal orbital angular momentum (OAM) carrying beams. The performance of such a system is estimated in terms of quantum bit error rate, outage capacity, and effective data rate taking into account the impact of error correction and privacy amplification. Based on the simulation of OAM-carrying beam propagating through atmospheric channels impaired by turbulence, the crosstalk among the multiplexed channels are investigated and its effect on the performance of the QKD system is evaluated. The presented results provide insight into the efficient design of such multiplexed QKD systems particularly in terms of the choice of the optimal average photon number per pulse and the multiplexing mode set.
Abstract Recently, there is a tremendous attention on the high-dimensional quantum information processing using the orbital angular momentum (OAM) of photons. It provides an efficient method to increase the capacity of quantum channel. However, OAM is very vulnerable to atmospheric turbulence, resulting in phase distortion and, therefore, leading to information leakage during quantum communications. On the other hand, quantum secure direct communications (QSDC) define an efficient way of information exchange through quantum channels directly. Here in this work, by combining the applications of OAM states of photons as the information carrier with the QSDC, we analyze the performance of the high-dimensional quantum secure direct communication protocol based on encoding the information on the single photon OAM state under the condition of free space channel. Numerically, we discussed the performance of OAM states QSDC under atmospheric turbulence, and mainly calculated the influence of cross-talk caused by phase fluctuation on the system. We draw the conclusion that under the weak turbulence, when the beam waist and the Fried parameter r become comparable, the information capacity will decrease sharply.