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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

An adaptation method to improve secret key rates of time-frequency QKD in atmospheric turbulence channels

Xiaole Sun, Ivan B. Djordjević, Mark Allen Neifeld

Published Mar 15, 2016• 4 citations
Publisher

Abstract

Free-space optical (FSO) channels can be characterized by random power fluctuations due to atmospheric turbulence, which is known as scintillation. Weak coherent source based FSO quantum key distribution (QKD) systems suffer from the scintillation effect because during the deep channel fading the expected detection rate drops, which then gives an eavesdropper opportunity to get additional information about protocol by performing photon number splitting (PNS) attack and blocking single-photon pulses without changing QBER. To overcome this problem, in this paper, we study a large-alphabet QKD protocol, which is achieved by using pulse-position modulation (PPM)-like approach that utilizes the time-frequency uncertainty relation of the weak coherent photon state, called here TF-PPM-QKD protocol. We first complete finite size analysis for TF-PPM-QKD protocol to give practical bounds against non-negligible statistical fluctuation due to finite resources in practical implementations. The impact of scintillation under strong atmospheric turbulence regime is studied then. To overcome the secure key rate performance degradation of TF-PPM-QKD caused by scintillation, we propose an adaptation method for compensating the scintillation impact. By changing source intensity according to the channel state information (CSI), obtained by classical channel, the adaptation method improves the performance of QKD system with respect to the secret key rate. The CSI of a time-varying channel can be predicted using stochastic models, such as autoregressive (AR) models. Based on the channel state predictions, we change the source intensity to the optimal value to achieve a higher secret key rate. We demonstrate that the improvement of the adaptation method is dependent on the prediction accuracy.

DOI
10.1117/12.2213035

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Free-space optical (FSO) channels can be characterized by random power fluctuations due to atmospheric turbulence, which is known as scintillation. Weak coherent source based FSO quantum key distribution (QKD) systems suffer from the scintillation effect because during the deep channel fading the expected detection rate drops, which then gives an eavesdropper opportunity to get additional information about protocol by performing photon number splitting (PNS) attack and blocking single-photon pulses without changing QBER. To overcome this problem, in this paper, we study a large-alphabet QKD protocol, which is achieved by using pulse-position modulation (PPM)-like approach that utilizes the time-frequency uncertainty relation of the weak coherent photon state, called here TF-PPM-QKD protocol. We first complete finite size analysis for TF-PPM-QKD protocol to give practical bounds against non-negligible statistical fluctuation due to finite resources in practical implementations. The impact of scintillation under strong atmospheric turbulence regime is studied then. To overcome the secure key rate performance degradation of TF-PPM-QKD caused by scintillation, we propose an adaptation method for compensating the scintillation impact. By changing source intensity according to the channel state information (CSI), obtained by classical channel, the adaptation method improves the performance of QKD system with respect to the secret key rate. The CSI of a time-varying channel can be predicted using stochastic models, such as autoregressive (AR) models. Based on the channel state predictions, we change the source intensity to the optimal value to achieve a higher secret key rate. We demonstrate that the improvement of the adaptation method is dependent on the prediction accuracy.
We optimize secret key rates (SKRs) of weak coherent pulse (WCP)-based quantum key distribution (QKD) over time-varying free-space optical channels affected by atmospheric turbulence. The random irradiance fluctuation due to scintillation degrades the SKR performance of WCP-based QKD, and to improve the SKR performance, we propose an adaptive scheme in which transmit power is changed in accordance with the channel state information. We first optimize BB84 and decoy state-based QKD protocols for different channel transmittances. We then present our adaptation method, to overcome scintillation effects, of changing the source intensity based on channel state predictions from a linear autoregressive model while ensuring the security against the eavesdropper. By simulation, we demonstrate that by making the source adaptive to the time-varying channel conditions, SKRs of WCP-based QKD can be improved up to over 20%.
Security issues of terrestrial free-space optical (FSO) communications over strong atmospheric turbulence are investigated. Based on a subcarrier intensity modulated FSO system model, we first study the scintillation reciprocity of the system from a coherence time perspective. A private secret key-based cryptosystem with key management is introduced to enhance FSO security, and a key agreement approach is proposed based on statistics of the random atmospheric turbulence-induced fading channel measurements. Secret key rate of the key agreement scheme is studied for the strong turbulence channel characterized by the K-distribution. Practical key agreement protocol is designed based on channel identification.
We devoted to analyzing information transfer in quantum channels in terms of the performance of quantum key distribution (QKD) free-space optical (FSO) communication systems through Bennett and Brassard 84 (BB84) protocol by taking into account the combined effect of attenuation, turbulence, pointing error, and angle of arrival (AOA) fluctuations. Path loss is modeled by Beer-Lambert law, and the turbulent channel is assumed to be Fisher-Snedecor F distributed. The pointing error and AOA fluctuations are modeled by Hoyt and Rayleigh distributions, respectively. The error and sift probabilities, quantum bit error rate, and secret key rate of a QKD FSO system are obtained in analytical form, and results are presented depending on various parameters. It is shown that increased beam waist, beam deviation, AOA fluctuations, and propagation distance cause performance degradation and less secure information transmission. However, an increase in the ratio of horizontal and vertical beam misalignments, field of view, average photon number per pulse, visibility of the atmospheric environment, and optical beam wavelength impact the performance of QKD FSO systems positively. The effect of the turbulence structure constant is observed to be modest on the performance of the QKD FSO system.
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.
We investigate the performance of relativistic quantum key distribution (RQKD) over turbulent free-space optical channels for both single-photon and coherent-state implementations. A theoretical model is developed to describe the effect of atmospheric turbulence on interferometric visibility and secret-key generation by incorporating turbulence-induced phase fluctuations into the key-rate analysis. Numerical simulations are performed under realistic channel conditions to evaluate the achievable communication distance and secret-key rate. The results show that atmospheric turbulence degrades the protocol performance by reducing interference visibility, with the severity of the degradation determined by the ratio between the interferometer-arm separation rrr (or temporal separation of signal and reference states ΔTΔTΔT) and Fried's parameter. The single-photon protocol remains operational over all investigated turbulence regimes, whereas the coherent-state implementation exhibits a critical dependence on the interferometer geometry (especially on ΔTΔTΔT), leading to a threshold beyond which secure key generation is no longer possible. These findings quantify the impact of atmospheric turbulence on relativistic quantum key distribution and provide practical guidelines for the design and optimization of free-space RQKD systems.
We study large-alphabet quantum key distribution (QKD) based on the use of weak-coherent states and the time–frequency uncertainty relation. The large alphabet is achieved by dividing time and spectrum into M bins resulting in a frame similar to traditional pulse-position modulation (in time domain). However, the non-uniform occurrence of a photon prepared in a time/frequency bin creates the space for eavesdropping. By analysis, we show that a new intercept-resend attack strategy exists, which is stronger than that has been reported in the literature and hence the secret key rate of time-frequency QKD (TF-QKD) can be more tightly bounded. We then analyse the secret key rates of TF-QKD under various practical issues, such as channel loss, background noise, jitter and atmospheric turbulence in order to better understand the applicability of TF-QKD. Further, we discuss the information reconciliation for TF-QKD. Specifically, we investigate the layered coding scheme for TF-QKD based on quasi-cyclic low-density parity-check codes against jitter and atmospheric turbulence. By simulation, we demonstrate that information reconciliation can be efficiently achieved.