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Acta Physica Sinica

Measurement-device-independent quantum key distribution under K-distributed strong atmospheric turbulence

Wen-Yuan Gu, Zhao Shang-hong, Chen Dong, Zhuo-Dan Zhu, Ya-Yun Qu

Published Jan 1, 2019• 3 citations
Publisher

Abstract

Free-space quantum key distribution (QKD) allows two distant parties to share secret keys with information-theoretic security, which can pave the way for satellite-ground quantum communication to set up a global network for sharing secret message. However, free-space channels in the presence of atmospheric turbulence are affected by losses and fluctuating transmissivity which further affect the quantum bit error rate and the secure key rate. To implement free-space QKD, it is indispensable to study the effect of atmospheric turbulence. Different models have been used to describe the probability distribution for channel transmission coefficient under atmospheric turbulence, including the log-normal distribution and K distribution. In this paper, we focus on free space measurement-device-independent quantum key distribution (MDI-QKD) under K-distributed strong atmospheric turbulence. The MDI-QKD can close all loopholes on detection and achieve a similar performance to QKD, relying on time-reversed version of entanglement-based QKD protocol. Threshold post-selection method is adopted to restrain detrimental effects of the atmospheric turbulence, which is based on the selection of the intervals with higher channel transmissivity. By combining the general MDI-QKD system model with this method, we present a framework for the optimal choice of threshold. Our simulation result shows that the optimal threshold is dependent on the turbulence intensity and expected channel loss. Furthermore, compared with the original MDI-QKD protocols, the proposed protocol with threshold post-selection method can acquire a considerable better performance in key rate, especially in regions of high turbulence and high loss. What is more, this is instructive to the building of a practical free-space MDI-QKD system with better performance.

DOI
10.7498/aps.68.20182130

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Free-space quantum key distribution (QKD) allows two distant parties to share secret keys with information-theoretic security, which can pave the way for satellite-ground quantum communication to set up a global network for sharing secret message. However, free-space channels in the presence of atmospheric turbulence are affected by losses and fluctuating transmissivity which further affect the quantum bit error rate and the secure key rate. To implement free-space QKD, it is indispensable to study the effect of atmospheric turbulence. Different models have been used to describe the probability distribution for channel transmission coefficient under atmospheric turbulence, including the log-normal distribution and K distribution. In this paper, we focus on free space measurement-device-independent quantum key distribution (MDI-QKD) under K-distributed strong atmospheric turbulence. The MDI-QKD can close all loopholes on detection and achieve a similar performance to QKD, relying on time-reversed version of entanglement-based QKD protocol. Threshold post-selection method is adopted to restrain detrimental effects of the atmospheric turbulence, which is based on the selection of the intervals with higher channel transmissivity. By combining the general MDI-QKD system model with this method, we present a framework for the optimal choice of threshold. Our simulation result shows that the optimal threshold is dependent on the turbulence intensity and expected channel loss. Furthermore, compared with the original MDI-QKD protocols, the proposed protocol with threshold post-selection method can acquire a considerable better performance in key rate, especially in regions of high turbulence and high loss. What is more, this is instructive to the building of a practical free-space MDI-QKD system with better performance.
Measurement-Device-Independent (MDI) QKD eliminates detector side channels in QKD and allows an untrusted relay between two users. A desirable yet highly challenging application is to implement MDI-QKD through free-space channels. One of the major factors that affect the secure key rate in free-space MDI-QKD is atmospheric turbulence. In this work we show two important results: First, the independent fluctuations of transmittances in the two channels can significantly reduce MDI-QKD performance due to turbulence-induced channel asymmetry. Second, we consider the Prefixed Real-Time Selection (P-RTS) method we formerly introduced to BB84 and extend it to MDI-QKD. Users can monitor classical transmittances in their channels and improve performance by post-selecting signals in real-time based on pre-calculated thresholds. We show that we can establish a 2-dimensional threshold between Alice and Bob to post-select signals with both high signal-to-noise ratio and low channel asymmetry in real time, and greatly extend the maximum range of MDI-QKD in the presence of turbulence, which can be an important step towards future free-space MDI-QKD experiments.
Real-world Bennett-Brassard 1984 quantum key distribution (QKD) systems utilize imperfect devices that introduce vulnerabilities to their security, known as side-channel attacks. Measurement-device-independent (MDI) QKD authorizes an untrusted third party to make measurements and removes all side-channel attacks. The typical implementations of MDI QKD employ nearly symmetric channels which are difficult to realize physically in many practical scenarios such as when asymmetric channel losses are present, normally a consequence of the communication environment. Maritime and satellite-based communications are two such instances in which the channels are characterized by continuously changing losses in different channels. In this work we perform asymmetric MDI QKD in a laboratory environment with simulated turbulence using an acousto-optic modulator to interrogate the performance of free-space quantum communication. Under turbulent conditions, scattering and beam wandering cause intensity fluctuations which decrease the detected signal-to-noise ratio. Using the seven-intensity optimization method proposed by Wang et al. [Phys. Rev. X 9, 041012 (2019)], coupled with prefixed-threshold real-time selection (PRTS), we demonstrate enhancement in the secure key rate under turbulent conditions for finite-size decoy-state MDI QKD. Furthermore, we show that PRTS can yield higher secure key rates, particularly in the high-loss regime.
Measurement-device-independent quantum key distribution (MDI-QKD), based on two-photon interference, is immune to all attacks against the detection system and allows a QKD network with untrusted relays. Since the MDI-QKD protocol was proposed, fiber-based implementations aimed at longer distance, higher key rates, and network verification have been rapidly developed. However, owing to the effect of atmospheric turbulence, MDI-QKD over a free-space channel remains experimentally challenging. Herein, by developing a robust adaptive optics system, high-precision time synchronization and frequency locking between independent photon sources located far apart, we realized the first free-space MDI-QKD over a 19.2-km urban atmospheric channel, which well exceeds the effective atmospheric thickness. Our experiment takes the first step toward satellite-based MDI-QKD. Moreover, the technology developed herein opens the way to quantum experiments in free space involving long-distance interference of independent single photons.
Reference-frame-independent quantum key distribution (RFI-QKD) can dispense with the requirements of active alignment on reference frames between legitimate users, which is beneficial for free-space implementation. However, the fluctuating transmittance due to atmospheric turbulence still remains a great challenge for improving the performance and has been seldom addressed. In this paper we extend the recently proposed prefixed-threshold real-time selection method to RFI-QKD while combining practical consideration of the transmittance probability distribution model based on the finite aperture theory. Through numerical simulations, we present an estimation for the variance of the log-normal model with respect to distance and receiving aperture radius, and demonstrate the effectiveness of using this method in the RFI protocol. Considering the finite-key effects, simulation results show that the gap of the key rate with different reference frame deviations can be alleviated by increasing the data size. By adopting this method one can tolerate more serious transmission loss, especially in strong turbulence cases, which is helpful for future free-space experimental designs.
Abstract The robustness of reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) against detection system vulnerabilities and its tolerance to reference frame drifts make it an ideal choice for hybrid channels. However, the impact of atmospheric turbulence on transmittance fluctuations remains a significant challenge for enhancing the performance of RFI-MDI-QKD. In this paper, we apply prefixed-threshold real-time selection and advantage distillation techniques to RFI-MDI-QKD in a hybrid channels scenario. Then, we analytically derive formulas for secret key rate in hybrid channels. Simulation results show that our modified scheme has apparent advances in both maximum tolerant loss and secure key rate compared to the fiber-only channel. Specifically, the result demonstrates that the maximum transmission distance can be improved by 15 km and 28 km when N = 1012 and 1011. Our work not only provides a more robust key distribution protocol but also establishes a solid theoretical foundation for enhancing the performance of RFI-MDI-QKD in hybrid channels.
Atmospheric turbulence poses a significant challenge to free-space measurement-device-independent quantum key distribution (FSO MDI-QKD) by inducing polarization decoherence and depolarization, which degrade the secret key rate (SKR). In this paper, we propose a unified depolarizing-dephasing channel model for turbulence-induced polarization decoherence in FSO MDI-QKD. This model consolidates phase perturbations, Gaussian beam spreading, beam drift, aperture truncation, and scintillation into closed-form parameters: depolarization factor, decoherence factor, and detection probability. By mapping turbulence to a von Mises-Fisher/Watson-distributed SU(2) rotation, we derive an analytic SKR expression compatible with existing MDI-QKD security analyses. The model excels in clear, overcast, and hazy weather conditions, offering computational efficiency and experimental verifiability for real-time link adaptation. Numerical simulations, illustrated on a ground-to-satellite free-space link, confirm its accuracy, enabling robust physical layer design for global-scale MDI-QKD networks.