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Entropy

Prefixed-Threshold Real-Time Selection for Free-Space Sending-or-Not Twin-Field Quantum Key Distribution

Yang Yu, Rui Xu, Le Wang, Qianping Mao, Shengmei Zhao

Published Feb 27, 2022• 4 citations
Publisher

Abstract

As a variant of the twin-field quantum key distribution (TF-QKD), the sending-or-not twin-field quantum key distribution (SNS TF-QKD) is famous for its higher tolerance of misalignment error, in addition to the capacity of surpassing the rate-distance limit. Importantly, the free-space SNS TF-QKD will guarantee the security of the communications between mobile parties. In the paper, we first discuss the influence of atmospheric turbulence (AT) on the channel transmittance characterized by the probability distribution of the transmission coefficient (PDTC). Then, we present a method called prefixed-threshold real-time selection (P-RTS) to mitigate the interference of AT on the free-space SNS TF-QKD. The simulations of the free-space SNS TF-QKD with and without P-RTS are both given for comparison. The results showed that it is possible to share the secure key by using the free-space SNS TF-QKD. Simultaneously, the P-RTS method can make the free-space SNS TF-QKD achieve better and more stable performance at a short distance.

DOI
10.3390/e24030344

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As a variant of the twin-field quantum key distribution (TF-QKD), the sending-or-not twin-field quantum key distribution (SNS TF-QKD) is famous for its higher tolerance of misalignment error, in addition to the capacity of surpassing the rate-distance limit. Importantly, the free-space SNS TF-QKD will guarantee the security of the communications between mobile parties. In the paper, we first discuss the influence of atmospheric turbulence (AT) on the channel transmittance characterized by the probability distribution of the transmission coefficient (PDTC). Then, we present a method called prefixed-threshold real-time selection (P-RTS) to mitigate the interference of AT on the free-space SNS TF-QKD. The simulations of the free-space SNS TF-QKD with and without P-RTS are both given for comparison. The results showed that it is possible to share the secure key by using the free-space SNS TF-QKD. Simultaneously, the P-RTS method can make the free-space SNS TF-QKD achieve better and more stable performance at a short distance.
Abstract Phase-matching quantum key distribution (PM-QKD), a practical version of twin-field quantum key distribution (TF-QKD), is able to surpass the linear bound without quantum repeaters. Implementing PM-QKD through free space can guarantee two parties to share unconditionally secure keys between ground stations and mobile platforms. However, atmospheric turbulence (AT) in the free-space channel would decrease the secure key rate (SKR) since it would cause fluctuations of transmittances. Two works we do are presented in this paper. First, for simplicity and generality, we derive the SKR for 4-intensity PM-QKD with asymmetric channel transmittances. Secondly, we apply the observable model of the prefixed-threshold real-time selection (P-RTS) method to mitigate the effect of AT in PM-QKD. Here, the authorized parties predetermine the threshold of transmittances and use it to select the signals while monitoring the real-time transmittances. The results show that the performance of PM-QKD in free space is severely degraded by AT, while P-RTS can reduce the impact of AT, making it transmit more than 3 times as long the distance and have a 3.37 times as large SKR at a distance of 50 km.
As a practical version of twin-field quantum key distribution (TF-QKD), phase-matching quantum key distribution (PM-QKD) is able to surpass the linear bound without quantum repeaters. Implementing PM-QKD through free space can guarantee two parties to share unconditionally secure keys between ground stations and mobile platforms. However, atmospheric turbulence decreases the free-space secure key rate as the result of fluctuations of transmittances caused by it. This paper includes two works we do. First, for generality, we derive the secure key rate formula of 4-intensity PM-QKD based on asymmetric channel transmittances. Second, we numerically simulate the performance of PM-QKD in free space and ideal circumstance to study the effect of the atmospheric turbulence.
In free-space quantum key distribution (QKD) in turbulent conditions, scattering and beam wandering cause intensity fluctuations which decrease the detected signal-to-noise ratio. This effect can be mitigated by rejecting received bits when the channel's transmittance is below a threshold. Thus, the overall error rate is reduced and the secure key rate increases despite the deletion of bits. In this work, we implement recently proposed selection methods focusing on the prefixed-threshold real-time selection (P-RTS) where a cutoff can be chosen prior to data collection and independently of the transmittance distribution. We perform finite-size decoy-state Bennett-Brassard 1984 QKD in a laboratory setting where we simulate the atmospheric turbulence using an acousto-optical modulator. We show that P-RTS can yield considerably higher secure key rates for a wide range of the atmospheric channel parameters. In addition, we evaluate the performance of the P-RTS method for a realistically finite sample size. We demonstrate that a near-optimal selection threshold can be predetermined even with imperfect knowledge of the channel transmittance distribution parameters.
Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because it can exceed the basic rate-distance limit without quantum repeaters. Its variant protocol, sending or not-sending quantum key distribution (SNS-QKD), not only fixes the security vulnerability of TF-QKD, but also can tolerate large misalignment errors. However, the current SNS-QKD protocol is based on the active decoy-state method, which may lead to side channel information leakage when multiple light intensities are modulated in practice. In this work, we propose a passive decoy-state SNS-QKD protocol to further enhance the security of SNS-QKD. Numerical simulation results show that the protocol not only improves the security in source, but also retains the advantages of tolerating large misalignment errors. Therefore, it may provide further guidance for the practical application of SNS-QKD.
Sending-or-not sending twin-field quantum key distribution (SNS TF-QKD) has the advantage of tolerating large amounts of misalignment errors, and its key rate can exceed the linear bound of repeaterless quantum key distribution. However, the weak randomness in a practical QKD system may lower the secret key rate and limit its achievable communication distance, thus compromising its performance. In this paper, we analyze the effects of the weak randomness on the SNS TF-QKD. The numerical simulation shows that SNS TF-QKD can still have an excellent performance under the weak random condition: the secret key rate can exceed the PLOB boundary and achieve long transmission distances. Furthermore, our simulation results also show that SNS TF-QKD is more robust to the weak randomness loopholes than the BB84 protocol and the measurement-device-independent QKD (MDI-QKD). Our results emphasize that keeping the randomness of the states is significant to the protection of state preparation devices.
Future quantum communication networks envisaged on a global scale will include various networks interlinked via optical fiber and free space channels. In recent years, quantum key distribution (QKD) protocol based on optical fiber has been extensively studied. Twin-field QKD (TF-QKD) may enable 550 km QKD using standard optical fiber without quantum repeaters. However, the performance of TF-QKD in free-space channel is still unclear. In this paper, a free-space channel model is proposed with specific turbulence characterization discussed. Here, the key rate of TF-QKD under multiple scenarios considering the variation of turbulence and different link configuration is investigated. Simulation results demonstrate that the performance of free-space TF-QKD is related to link configuration and turbulence motion which is determined by surface feature, time and height. Furthermore, TF-QKD protocol is a potential scheme for the free-space quantum communication.