Discrete-modulated Continuous-variable Quantum Key Distribution Research Articles

Trusted-source-noise model of discrete-modulated continuous-variable quantum key distribution

Trusted-source-noise model of discrete-modulated continuous-variable quantum key distribution

Amplitude-boosting attack against practical discrete-modulated continuous-variable quantum key distribution

Discrete-modulated continuous-variable quantum key distribution offers significant practical deployment advantages due to its straightforward state preparation and high compatibility with coherent optical communication systems. However, security analysis and parameter estimation of discrete-modulated protocol are different with Gaussian-modulated protocols, which could cause different practical security problems. Herein, we investigate the amplitude-boosting attack against discrete-modulated continuous-variable quantum key distribution systems and assess its impact on system performance. Our findings reveal that this attack could cause overestimation of secret key rate perceived by Alice and Bob, thereby opening a security loophole, and the vulnerability could be severer than Gaussian modulation. Additionally, we summarize defensive countermeasures, marking a crucial step towards enhancing the practical security of discrete-modulated continuous-variable quantum key distribution.

Security of discrete-modulated continuous-variable quantum key distribution

Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of 0.1−10−4 bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of 10 Gbits of secret key after n∼1011 rounds and distances of few tens of kilometres.

Quantum Hacking Against Discrete-Modulated Continuous-Variable Quantum Key Distribution Using Modified Local Oscillator Intensity Attack with Random Fluctuations

Quantum Hacking Against Discrete-Modulated Continuous-Variable Quantum Key Distribution Using Modified Local Oscillator Intensity Attack with Random Fluctuations

High-performance long-distance discrete-modulation continuous-variable quantum key distribution.

We experimentally demonstrate a high-rate discretely modulated continuous-variable quantum key distribution over 80-km standard single-mode fiber with a 2.5 Gbaud, 16-symbol, two-ring constellation. With the help of well-designed digital signal processing algorithms, the excess noise of the system can be effectively suppressed. The achieved secret key rates are 49.02 Mbits/s, 11.86 Mbits/s, and 2.11 Mbits/s over 25-km, 50-km, and 80-km optical fiber, respectively, and achieve 67.4%, 70.0%, and 66.5% of the secret key rate performance of a Gaussian-modulated protocol. Our work shows that it is feasible to build a high-performance, long-distance continuous-variable quantum key distribution system with only a small constellation size.

Discrete-modulation continuous-variable quantum key distribution with a high key rate

Discrete-modulation continuous-variable (CV) quantum key distribution has the potential for large-scale deployment in secure quantum communication networks owing to its low implementation complexity and compatibility with the current coherent optical telecommunication. However, current discrete-modulation protocols require relatively large constellation sizes to achieve a key rate comparable to that of the Gaussian modulation. Here, we show that a high key rate comparable to the Gaussian modulation can be achieved using only ten or so coherent states by implementing suitable key map and numerical convex optimization techniques. Specifically, the key rate of the two-ring constellation with 12 coherent states (four states in the inner ring and eight states in the outer ring) can reach 2.4 times of that of original quadrature phase shift keying and 70% of the Gaussian modulation protocol at 50 km. Such an approach can easily be applied to existing systems, making the discrete-modulation protocol an attractive alternative for high-rate and low-cost applications in secure quantum communication networks.

Theoretical development of discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution offers simple, stable and easy-to-implement key distribution systems. The discrete modulation scheme further reduces the technical difficulty. The main regret is that the security of discrete modulation schemes has not been sufficiently demonstrated. Schemes with different signal state distributions use various physical conditions to obtain the key rate formula, resulting in different security levels, computation complexities and implementation difficulties. Therefore, a relatively systematic and logically consistent security proof against most general attacks is worth exploring. On the other hand, extending the discrete modulation scheme and its variants to different applications, such as satellite-to-earth communication, can further activate and advance this field. Here, we briefly review the achievements that have been made in discrete-modulated continuous-variable quantum key distribution, and openly discuss some issues worthy of further research.

Experimental demonstration of high-rate discrete-modulated continuous-variable quantum key distribution system.

A high-rate continuous-variable quantum key distribution (CV-QKD) system based on high-order discrete modulation is experimentally investigated. With the help of the novel system scheme, effective digital signal processing (DSP) algorithms and advanced analytical security proof methods, the transmission results of 5.059 km, 10.314 km, 24.490 km, and 50.592 km are achieved for 1 GBaud optimized quantum signals. Correspondingly, the asymptotic secret key rates (SKRs) are 292.185 Mbps, 156.246 Mbps, 50.491 Mbps, and 7.495 Mbps for discrete Gaussian (DG) 64QAM, and 328.297 Mbps, 176.089 Mbps, 51.304 Mbps, and 9.193 Mbps for DG 256QAM, respectively. Under the same parameters, the achieved SKRs of DG 256QAM is almost same as ideal Gaussian modulation. In this case, the demonstrated high-rate discrete-modulated CV-QKD system has the application potential for high-speed security communication under tens of kilometers.

Neural network-based prediction of the secret-key rate of quantum key distribution

Numerical methods are widely used to calculate the secure key rate of many quantum key distribution protocols in practice, but they consume many computing resources and are too time-consuming. In this work, we take the homodyne detection discrete-modulated continuous-variable quantum key distribution (CV-QKD) as an example, and construct a neural network that can quickly predict the secure key rate based on the experimental parameters and experimental results. Compared to traditional numerical methods, the speed of the neural network is improved by several orders of magnitude. Importantly, the predicted key rates are not only highly accurate but also highly likely to be secure. This allows the secure key rate of discrete-modulated CV-QKD to be extracted in real time on a low-power platform. Furthermore, our method is versatile and can be extended to quickly calculate the complex secure key rates of various other unstructured quantum key distribution protocols.

Hide and seek with quantum resources: new and modified protocols for quantum steganography

Steganography is the science of hiding and communicating a secret message by embedding it in an innocent looking text such that the eavesdropper is unaware of its existence. Previously, attempts were made to establish steganography using quantum key distribution (QKD). Recently, it has been shown that such protocols are vulnerable to a certain steganalysis attack that can detect the presence of the hidden message and suppress the entire communication. In this work, we elaborate on the vulnerabilities of the original protocol which make it insecure against this detection attack. Further, we propose a novel steganography protocol using discrete modulation continuous variable QKD that eliminates the threat of this detection-based attack. Deriving from the properties of our protocol, we also propose modifications in the original protocol to dispose of its vulnerabilities and make it insusceptible to steganalysis.

Automated machine learning for secure key rate in discrete-modulated continuous-variable quantum key distribution

Continuous-variable quantum key distribution (CV QKD) with discrete modulation has attracted increasing attention due to its experimental simplicity, lower-cost implementation and compatibility with classical optical communication. Correspondingly, some novel numerical methods have been proposed to analyze the security of these protocols against collective attacks, which promotes key rates over one hundred kilometers of fiber distance. However, numerical methods are limited by their calculation time and resource consumption, for which they cannot play more roles on mobile platforms in quantum networks. To improve this issue, a neural network model predicting key rates in nearly real time has been proposed previously. Here, we go further and show a neural network model combined with Bayesian optimization. This model automatically designs the best architecture of neural network computing key rates in real time. We demonstrate our model with two variants of CV QKD protocols with quaternary modulation. The results show high reliability with secure probability as high as 99.15% - 99.59%, considerable tightness and high efficiency with speedup of approximately 107 in both cases. This inspiring model enables the real-time computation of unstructured quantum key distribution protocols' key rate more automatically and efficiently, which has met the growing needs of implementing QKD protocols on moving platforms.

Homodyne Detection Quadrature Phase Shift Keying Continuous-Variable Quantum key Distribution with High Excess Noise Tolerance

Discrete-modulated continuous-variable quantum key distribution with homodyne detection is widely recognized for its ease of implementation, efficiency with respect to error correction, and its compatibility with modern optical communication devices. However, recent studies report that the application of homodyne detection obtains poor tolerance to excess noise and insufficient transmission distance, hence seriously restricting the large-scale deployment of quantum secure communication networks. In this paper, we propose a homodyne detection protocol using the quadrature phase shift keying technique. By limiting information leakage, our proposed protocol enhances excess noise tolerance to a high level. Furthermore, we demonstrate that homodyne detection performs better than heterodyne detection in quaternary-modulated continuous-variable quantum key distribution under the untrusted detector noise scenario. The security is analyzed using the tight numerical method against collective attacks in the asymptotic regime. Our results imply that the current protocol is able to distribute keys in nearly intercity area and thus paves the way for constructing low-cost quantum secure communication networks.

Secret key rate of multi-ring M-APSK continuous variable quantum key distribution.

Discrete modulation continuous variable quantum key distribution (DM-CV-QKD) is highly considered in real implementations to avoid the complexity of Gaussian modulation (GM), which is optimum in terms of the key rate. DM-CV-QKD systems usually consider M-symbol phase shift keying (M-PSK) constellations. However, this type of constellation cannot reach transmission distances and key rates as high as GM, limiting the practical implementation of CV-QKD systems. Here, by considering M-symbol amplitude and phase shift keying (M-APSK) constellations, we can approximate GM. Indeed, considering finite-size effects, 4 ring 64-APSK can reach 52.0 km, only 7.2 km less than GM and 282% the maximum achievable transmission distance for 8-PSK.

Asymptotic security of discrete-modulation protocols for continuous-variable quantum key distribution

We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.

Trusted Detector Noise Analysis for Discrete Modulation Schemes of Continuous-Variable Quantum Key Distribution

Discrete-modulated continuous-variable quantum key distribution protocols are promising candidates for large-scale deployment due to the large technological overlap with deployed modern optical communication devices. The security of discrete modulation schemes has previously analyzed in the ideal detector scenario in the asymptotic limit. In this work, we calculate asymptotic key rates against collective attacks in the trusted detector noise scenario. Our results show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to ideal detectors.

Lengthening Transmission Distance of Continuous Variable Quantum Key Distribution with Discrete Modulation through Photon Catalyzing

Establishing global secure networks is a potential implementation of continuous-variable quantum key distribution (CVQKD) but it is also challenged with respect to long-distance transmission. The discrete modulation (DM) can make up for the shortage of transmission distance in that it has a unique advantage against all side-channel attacks; however, its further performance improvement requires source preparation in the presence of noise and loss. Here, we consider the effects of photon catalysis (PC) on the DM-involved source preparation for improving the transmission distance. We address a zero-photon-catalysis (ZPC)-based source preparation for enhancing the DM–CVQKD system. The statistical fluctuation is taken into account for the practical security analysis. Numerical simulations show that the ZPC-based source preparation can not only achieve the long-distance transmission, but also contributes to the reasonable increase of the secret key rate.

Discrete-Modulation Continuous-Variable Quantum Key Distribution Enhanced by Quantum Scissors

It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive.

Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution over Seawater Channel

We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the eight-state protocol in asymptotic and finite-size cases is analyzed in detail. Simulation results illustrate that the more complex is the seawater composition, the worse is the performance of the protocol. For different types of seawater channels, we can improve the performance of the protocol by selecting different optimal modulation variances and controlling the extra noise on the channel. Besides, we can find that the performance of the eight-state protocol is better than that of the four-state protocol, and there is little difference between homodyne detection and heterodyne detection. Although the secret key rate of the protocol that we propose is still relatively low and the maximum transmission distance is only a few hundred meters, the research on CV-QKD over the seawater channel is of great significance, which provides a new idea for the construction of global secure communication network.

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

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.

State-discrimination attack on discretely modulated continuous-variable quantum key distribution

The continuous-variable quantum key distribution (CVQKD) schemes with discrete modulation are proposed to allow distributions of secret keys over long distance due to the sharing of discrete data. However, the nonorthogonal signal states in these schemes can be discriminated by using quantum receivers with low error rates, which may incur state-discrimination (SD) attacks. We consider the feasibility of Eve's attacks on discrete-modulated CVQKD protocol based on the SD receiver. In particular, an intercept-resend attack is proposed on the four-state protocol based on an SD receiver and a heralded noiseless linear amplifier. The security analysis shows that the secret key rate inferred by Alice and Bob can be larger than its true value, which reveals that the original four-state protocol is not secure under the SD attack. Fortunately, the decoy states can be well applied to remedy this defect, but with the cost of complicated practical implementation.