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Mathematics

Adaptive Continuous-Variable Quantum Key Distribution with Discrete Modulation Regulative in Free Space

Yiwu Zhu, Lei Mao, Hui Hu, Yijun Wang, Ying Guo

Published Nov 25, 2022• 5 citations
Publisher

Abstract

The finite sampling bandwidth of an analog-to-digital converter has a negative effect on the continuous-variable quantum key distribution (CVQKD), which leaves a potential loophole for an eavesdropper and weakens the practical security of the system. To compensate for the loss in free space, we deploy an adaptive optics (AO) unit in the detector of the CVQKD system with discrete modulations. Since the closed-loop control bandwidth of the embedded AO unit can be optimized with the sampling frequency, the practical security of the system can be enhanced in terms of the secret key rate. The security analysis is demonstrated on the basis of the derived secret key rate with numerical simulations, providing a feasible implementation of CVQKD in realistic free-space environments.

DOI
10.3390/math10234450

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The finite sampling bandwidth of an analog-to-digital converter has a negative effect on the continuous-variable quantum key distribution (CVQKD), which leaves a potential loophole for an eavesdropper and weakens the practical security of the system. To compensate for the loss in free space, we deploy an adaptive optics (AO) unit in the detector of the CVQKD system with discrete modulations. Since the closed-loop control bandwidth of the embedded AO unit can be optimized with the sampling frequency, the practical security of the system can be enhanced in terms of the secret key rate. The security analysis is demonstrated on the basis of the derived secret key rate with numerical simulations, providing a feasible implementation of CVQKD in realistic free-space environments.
Practical security of the continuous-variable quantum key distribution (CVQKD) system with finite sampling bandwidth of analog-to-digital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.
Continuous-variable quantum key distribution (CVQKD) is an important application of quantum technology, which enables long-distance communicating parties to establish a string of unconditionally secure keys in an insecure environment. However, in a practical CVQKD system, the finite sampling bandwidth of the analog-to-digital converter (ADC) at the receiver may create inaccurate sampling results, leading to errors in parameter estimation process and leaving a security loophole for eavesdroppers. In order to eliminate the finite sampling bandwidth effect, we propose a peak-compensation-based CVQKD scheme, which estimates the discrepancy between the maximum sampling value and the peak value of each pulse based on the characteristics of Gaussian pulse. The maximum sampling values are compensated by the estimated discrepancy, so that the legitimate parties can obtain correct sampling results. We analyze the influence of the finite sampling bandwidth on the security of the system, expounding the specific steps of peak-compensation, comparing the estimated excess noise before and after peak-compensation, and discussing the security of the system under Gaussian collective attacks. Simulation results show that this scheme can greatly improve the accuracy of pulse peak sampling and remove the finite sampling bandwidth effect. Moreover, the channel parameters estimated by the communicating parties are also corrected by using the compensated values. Compared with the scheme without peak-compensation, this scheme eliminates the limitation of the system repetition to the secret key bit rate, and has longer secure transmission distance and higher secret key bit rate. In addition, compared with other methods of solving the finite sampling bandwidth effect, the proposed scheme can be directly implemented in data processing stage after sampling without any additional devices, and thus increasing no complexity of the system.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
Abstract The excess noise inducing in the process of the quantum communication procedure is the major obstacle restricting the performance of continuous-variable quantum key distribution (CVQKD). In order to effectively suppress the excess noise through correcting the propagation-induced distortions on the quality of the propagated quantum signal, we propose a general scheme of suppressing excess noise for CVQKD via adaptive optics (AO) approach. The analysis shows that phase-only AO compensation exhibits excellent performance in controlling the excess noise, which is embodied in substantially extending the secure propagation distance and improving the secret key rate of the system. And thereby the development and improvement of AO has the potential advantage to break the distance constraints due to the excess noise results from propagation-dominated factors. Our scheme provides a feasible method for further implementation of practical large-scale CVQKD.
In a practical continuous-variable quantum key distribution (CVQKD) system, the optical attenuator can adjust the Gaussian-modulated coherent states and the local oscillator signal to an optimal value for guaranteeing the security of the system and optimizing the performance of the system. However, the performance of the optical attenuator may deteriorate due to the intentional and unintentional damage of the device. In this paper, we investigate the practical security of a CVQKD system with reduced optical attenuation. We find that the secret key rate of the system may be overestimated based on the investigation of parameter estimation under the effects of reduced optical attenuation. This opens a security loophole for Eve to successfully perform an intercept-resend attack in a practical CVQKD system. To close this loophole, we add an optical fuse at Alice's output port and design a scheme to monitor the level of optical attenuation in real time, which can make the secret key rate of the system evaluated precisely. The analysis shows that these countermeasures can effectively resist this potential attack.
An amplitude modulator plays an essential role in the implementation of continuous-variable quantum key distribution (CVQKD), whereas it may bring about a potential security loophole in the practical system. The high-frequency modulation of the actual transmitter usually results in the high rate of the system. However, an imperfect amplitude modulator (AM) can give birth to a potential information leakage from the modulation of the transmitter. To reveal a potential security loophole from the high-frequency AM embedded in the transmitter, we demonstrate an influence on the practical security of the system in terms of the secret key rate and maximal transmission distance. The results indicate the risk of this security loophole in the imperfect AM-embedded transmitter. Fortunately, the legal participants can trace back the potential information leakage that has been produced from the imperfect transmitter at high frequencies, which can be used for defeating the leakage attack in CVQKD. We find the limitations of the imperfect AM-embedded transmitter of the high-frequency quantum system, and hence, we have to trade off the practical security and the modulation frequency of the AM-embedded transmitter while considering its implementation in a practical environment.