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Optical Engineering

Discrete-modulated continuous-variable quantum key distribution with a machine-learning-based detector

Jiawei Li, Ying Guo, Xudong Wang, Cailang Xie, Ling Zhang, Duan Huang

Published Jun 14, 2018• 14 citations
Publisher

Abstract

The discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) could break the distance limitation of Gaussian-modulated CV-QKD. In practice, the high-performance error correction code plays an important role in DM-CV-QKD and affects the secure transmission distance. However, DM-CV-QKD usually works under low signal-to-noise ratio (SNR) and the design of high-performance error correction code under this condition is difficult, so that it would impose a limitation on further improvement of the secure distance. We propose a DM-CV-QKD with the machine-learning-based detector to further improve the secure distance. The numerical result shows that the proposed scheme could validly improve the system performance. Viewed from another perspective, the proposed scheme could be employed to overcome various impairments induced by the channel and thereby lower the demand of error correction codes on the SNR threshold of the quantum channel without compromising the system performance. The proposed scheme opens the door to applying machine leaning to directly process the raw secret key and improve the performance for CV-QKD systems.

DOI
10.1117/1.oe.57.6.066109

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The discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) could break the distance limitation of Gaussian-modulated CV-QKD. In practice, the high-performance error correction code plays an important role in DM-CV-QKD and affects the secure transmission distance. However, DM-CV-QKD usually works under low signal-to-noise ratio (SNR) and the design of high-performance error correction code under this condition is difficult, so that it would impose a limitation on further improvement of the secure distance. We propose a DM-CV-QKD with the machine-learning-based detector to further improve the secure distance. The numerical result shows that the proposed scheme could validly improve the system performance. Viewed from another perspective, the proposed scheme could be employed to overcome various impairments induced by the channel and thereby lower the demand of error correction codes on the SNR threshold of the quantum channel without compromising the system performance. The proposed scheme opens the door to applying machine leaning to directly process the raw secret key and improve the performance for CV-QKD systems.
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Continuous variable quantum key distribution (CV-QKD) allows the distribution of symmetric keys in a secure manner. CV-QKD systems can extract keys at its maximum rate when using Gaussian modulation (GM). Nonetheless, GM demands high-capacity random number sources and tends to be very hard to approach in practice. To circumvent these disadvantages, higher-order probabilistic -shaped discrete modulation (DM) can be used. State-of-the-art works compute the key rates of DM-CV-QKD systems considering a fixed value for the reconciliation efficiency and do not take into account the frame error rate (FER) of the system, thus over or under estimating the key rates. In this work, we study the security bounds of CV-QKD systems considering probabilistic shaped DM formats with 256-symbols in the finite-size regime. This accounting for the true value of the reconciliation efficiency, and the FER of the information reconciliation step. Both conventional and hexagonal 256-quadrature amplitude modulation (QAM) constellations yield higher key rates than 256-amplitude and phase shift keying (APSK) constellations, with 256-QAM constellations being indistinguishable in performance with GM for high transmission distances. Minimum signal-to-noise ratio (SNR) values were fixed from a FER analysis through a CV-QKD simulation allowing for key extraction considering different FER levels. Lower FER values are associated with higher SNRs in the system and thus lower achievable transmission distances. Nonetheless, the FER maximizing the extraction key rate is not null. Our results show that the extraction key rate is maximized by SNR adjustment which should have in account both the reconciliation efficiency and the FER.
Continuous-variable quantum key distribution (CV-QKD) with discrete modulation has received widespread attentions because of its experimental simplicity, lower-cost implementation and ease to multiplex with classical optical communication. Recently, some inspiring numerical methods have been applied to analyse the security of discrete-modulated CV-QKD against collective attacks, which promises to obtain considerable key rate over one hundred kilometers of fiber distance. However, numerical methods require up to ten minutes to calculate a secure key rate one time using a high-performance personal computer, which means that extracting the real-time secure key rate is impossible for discrete-modulated CV-QKD system. Here, we present a neural network model to quickly predict the secure key rate of homodyne detection discrete-modulated CV-QKD with good accuracy based on experimental parameters and experimental results. With the excess noise of about 0.010.010.01, the speed of our method is improved by about seven orders of magnitude compared to that of the conventional numerical method. Our method can be extended to quickly solve complex security key rate calculation of a variety of other unstructured quantum key distribution protocols.
Continuous-variable quantum key distribution (CV-QKD) is realized with coherent detection and is therefore very suitable for a cost-efficient implementation. The major challenge in CV-QKD is mitigation of laser phase noise at a signal to noise ratio of much less than 0 dB. So far, this has been achieved with a remote local oscillator or with auxiliary signals. For the first time, we experimentally demonstrate that CV-QKD can be performed with a real local oscillator and without auxiliary signals which is achieved by applying Machine Learning methods. It is shown that, with the most established discrete modulation protocol, the experimental system works down to a quantum channel signal to noise ratio of -19.1 dB. The performance of the experimental system allows CV-QKD at a key rate of 9.2 Mbit/s over a fiber distance of 26 km. After remote local oscillator and auxiliary signal aided CV-QKD, this could mark a starting point for a third generation of CV-QKD systems that are even more attractive for a wide implementation because they are almost identical to standard coherent systems.
To overcome the low reconciliation efficiency problem of Gaussian modulation (GM)-based-continuous variable (CV)-quantum key distribution (QKD), in this paper, we propose to use discretized GM (DGM)-based-CV-QKD. The proposed CV-QKD scheme has complexity and reconciliation efficiency similar to that of discrete modulation (DM)-based-CV-QKD and at the same time solves for the problem of the nonexistence of strict security proofs for the DM-CV-QKD under the collective attacks. We demonstrate that the 32-points-based DGM CV-QKD can closely approach the theoretical SKR-limit in medium and high channel losses regimes. On the other hand, the 64-points-based DGM CV-QKD scheme closely approaches the SKR-limit for all channel losses.
Continuous-variable quantum key distribution (CV-QKD) with a real local oscillator (LO) experiences a phase attack security challenge due to the reference pulses transmitted along with quantum signals over an unsecure quantum channel. In this paper, a phase attack on reference pulses of CV-QKD with a real LO is investigated. The performance of the discrete-modulated (DM) CV-QKD under this attack is analyzed analytically and by simulation, and compared with the Gaussian-modulated (GM) CV-QKD. It is found that such an attack by an eavesdropper's, significantly reduce the transmission distance for the GM based CV-QKD, whereas, the DM based CV-QKD shows a high tolerance to high phase noise. Based on phase attack monitoring, a new adaptive modulation scheme is proposed for CV-QKD to adaptively switch between GM and DM so as to maintain the optimum secret key rate.