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Journal of Modern Optics

Weak-coherent-state-based time-frequency quantum key distribution

Yequn Zhang, Ivan B. Djordjević, Mark Allen Neifeld

Published Aug 18, 2015• 7 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2015.1075616

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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.
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.
The discrete-variables (DV) time-frequency (TF) quantum key distribution (QKD) protocol is a BB84-like protocol, which utilizes time and frequency as complementary bases. As orthogonal modulations, pulse position modulation (PPM) and frequency shift keying (FSK) are capable of transmitting several bits per symbol, i.e., per photon. However, unlike traditional binary polarization shift keying, PPM and FSK do not allow perfectly complementary bases. So information is not completely deleted when the wrong-basis filters are applied. Since a general security proof does not yet exist, we numerically assess DV-TF-QKD. We show that the secret key rate increases with a higher number of symbols per basis. Further we identify the optimal pulse relations in the two bases in terms of key rate and resistance against eavesdropping attacks.
Large-scale quantum communication networks are still a huge challenge due to the rate-distance limit of quantum key distribution (QKD). Recently, twin-field (TF) QKD has been proposed to overcome this limit. Here, we prove that coherent-state-based TF-QKD is a time-reversed entanglement protocol, where the entanglement generation is realized with entanglement swapping operation via an entangled coherent state measurement. We propose a coherent-state-based TF-QKD with optimal secret key rate under symmetric and asymmetric channels by using coherent state and cat state coding. Furthermore, we show that our protocol can be converted to all recent coherent-state-based TF-QKD protocols by using our security proof. By using the entanglement purification with two-way classical communication, we improve the transmission distance of all coherent-state-based TF-QKD protocols.
Quantum key distribution is a quantum communication protocol which seeks to address potential vulnerabilities in data transmission and storage. One of the main challenges in the field is achieving high rates of secret key in lossy and turbulent free-space channels. In this scenario, most experimental demonstrations have used the polarization of photons as their qubit carriers, due to the relative robustness of polarization in free-space propagation. Time-bin or phase-based protocols are considered less practical due to the wave-front distortion caused by atmospheric turbulence. However, demonstrations of novel free-space interferometer designs are enabling interferometers to measure multimodal signals with high visibility. That means it is now viable to consider the prospects of implementing time-bin or phase-based protocols, which have demonstrated high key rates and long transmission distances in optical fiber. In this work, we present the possibilities of implementing time-bin protocols in turbulent free-space channels, using the coherent one-way protocol as the example. We present an analysis of the secret key rate and quantum bit error rate of the system, providing the errors due to noise counts, and the extinction ratio of the pulses. Finally, we developed a model to quantify the expected losses for a turbulence free-space channel, specifically for a free-space satellite-to-ground station channel.
Twin-field quantum key distribution (TF-QKD) has emerged as a promising solution for practical quantum communication over long-haul fiber. However, previous demonstrations on TF-QKD require the phase locking technique to coherently control the twin light fields, inevitably complicating the system with extra fiber channels and peripheral hardware. Here, we propose and demonstrate an approach to recover the single-photon interference pattern and realize TF-QKD without phase locking. Our approach separates the communication time into reference frames and quantum frames, where the reference frames serve as a flexible scheme for establishing the global phase reference. To do so, we develop a tailored algorithm based on fast Fourier transform to efficiently reconcile the phase reference via data postprocessing. We demonstrate no-phase-locking TF-QKD from short to long distances over standard optical fibers. At 50-km standard fiber, we produce a high secret key rate (SKR) of 1.27 Mbit/s, while at 504-km standard fiber, we obtain the repeaterlike key rate scaling with a SKR of 34 times higher than the repeaterless secret key capacity. Our work provides a scalable and practical solution to TF-QKD, thus representing an important step towards its wide applications.
Long-distance quantum key distribution (QKD) has long time seriously relied on trusted relay or quantum repeater, which either has security threat or is far from practical implementation. Recently, a solution called twin-field (TF) QKD and its variants have been proposed to overcome this challenge. However, most security proofs are complicated, a majority of which could only ensure security against collective attacks. Until now, the full and simple security proof can only be provided with asymptotic resource assumption. Here, we provide a composable finite-key analysis for coherent-state-based TF-QKD with rigorous security proof against general attacks. Furthermore, we develop the optimal statistical fluctuation analysis method to significantly improve secret key rate in high-loss regime. The results show that coherent-state-based TF-QKD is practical and feasible, with the potential to apply over nearly one thousand kilometers.