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Optics Express

Rigorous calibration of homodyne detection efficiency for continuous-variable quantum key distribution

Mi Zou, Yingqiu Mao, Teng‐Yun Chen

Published May 29, 2022• 12 citations
Publisher

Abstract

We propose a rigorous calibration method for homodyne detection efficiency, which combines all the factors that affect detection efficiency to calibrate together through the actual homodyne detection. With this method, the transmittance converted from electronic noise in the one-time calibration method of the shot noise can be attributed to the detection inefficiency. Thus, a trusted detection noise-free model for continuous-variable quantum key distribution (CV-QKD) can be established, which simplifies the calibration of shot noise while having the same performance as the trusted detection noise model. We demonstrate this calibration method with a balanced detector based on a transimpedance amplifier. Experimental results show that detection efficiency will be overestimated if the integration factor of the detector is overlooked. The overestimation of the detection efficiency leads to an underestimation of modulation variance and excess noise when the modulation variance is monitored by the balanced detector, which opens security loopholes. Our method may prove a necessary method in the calibration of detection efficiency for CV-QKD.

DOI
10.1364/oe.461680

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We propose a rigorous calibration method for homodyne detection efficiency, which combines all the factors that affect detection efficiency to calibrate together through the actual homodyne detection. With this method, the transmittance converted from electronic noise in the one-time calibration method of the shot noise can be attributed to the detection inefficiency. Thus, a trusted detection noise-free model for continuous-variable quantum key distribution (CV-QKD) can be established, which simplifies the calibration of shot noise while having the same performance as the trusted detection noise model. We demonstrate this calibration method with a balanced detector based on a transimpedance amplifier. Experimental results show that detection efficiency will be overestimated if the integration factor of the detector is overlooked. The overestimation of the detection efficiency leads to an underestimation of modulation variance and excess noise when the modulation variance is monitored by the balanced detector, which opens security loopholes. Our method may prove a necessary method in the calibration of detection efficiency for CV-QKD.
Abstract The time-domain balanced homodyne detector (TBHD) is critical component in continuous-variable quantum key distribution (CVQKD). The shot-noise-limited attribute of a TBHD depends on the whole spectrum of detector, in contrast to a frequency-domain balanced homodyne detector that focuses only on part of the spectrum. We propose a method for accurate calibration of the shot-noise-limited attribute of the TBHD by overlapping the gain lines of the TBHD and an integrated photodetector. The overlapping of two lines indicates that the detector is indeed shot noise limited, which is crucial to the security of CVQKD. Experimentally, we use this method to obtain a calibration error of ±1‰. Theoretical analysis showed that the CVQKD performance is very sensitive to calibration errors of shot noise, and proper countermeasures should be employed to eliminate this issue. The presented methods are expected to contribute to CVQKD security and TBHD standardization.
The shot-noise unit in continuous-variable quantum key distribution plays an important and fundamental role in experimental implementation, as it is used as a normalization parameter that contributes to performing security analyses and distilling key information. However, the traditional calibration procedure and detector model cannot cover all system noise in practical applications, which results in loopholes and influences the practical security. What is more, the traditional procedure is also rather complicated and has difficulty in providing compatibility with automatic operating systems. In this paper, we propose a calibration model based on a proposed trusted detector model, which could naturally close the loopholes in practical applications. It can help to identify the shot-noise unit in only one step, which can not only effectively simplify the evaluation process but also reduce the statistical fluctuations, while two steps are needed in the traditional method. We prove its feasibility and derive a complete version of the corresponding entanglement-based model. A detailed security analysis against arbitrary collective attacks and numerous simulation results in both the asymptotic-limit regime and the finite-size regime are provided. A proof-of-principle experiment is implemented, and the results indicate that our one-time calibration model can be employed as a powerful alternative method for calibrating the shot-noise unit. Our method paves the way for the deployment of continuous-variable quantum key distribution with real-time calibration and automatic operation.
Abstract The practical homodyne detector model of continuous-variable quantum key distribution models the inherent imperfections of the practical homodyne detector, namely the limited detection efficiency and the electronic noise, into trusted loss. However, the conventional practical homodyne detector model is valid only when both the imperfections of the practical homodyne detector are calibrated. In this paper, we show a modified practical homodyne detector model that can model the imperfections separately. The phase-sensitive amplifier (PSA) is further applied to compensate the imperfections of the practical homodyne detector. The feasibility of the modified practical homodyne detector model with the PSA is proved and the security analysis is provided in detail. Simulation results reveal that the PSA can be used to improve the performance of the modified practical homodyne detector model, and when the gain is infinitely high, the limited detection efficiency can be fully compensated.
Imperfections in practical detectors, including limited detection efficiency, and inherent electronic noise, can seriously decrease the transmission distance of continuous-variable measurement-device-independent quantum key distribution systems. Owing to the difficulties inherent in realizing a high-efficiency fiber homodyne detector, challenges still exist in continuous-variable measurement-device-independent quantum key distribution system implementation. We offer an alternative approach in an attempt to solve these difficulties and improve the potential for system implementation. Here, a novel practical detector modeling method is utilized, which is combined with a one-time shot-noise-unit calibration method for the purpose of system realization. The new modeling method benefits greatly from taking advantage of one-time shot-noise-unit calibration methods, such as measuring electronic noise and shot noise directly to a novel shot-noise unit, so as to eliminate the statistical fluctuations found in previous methods; this makes the implementation of such systems simpler, and the calibration progress more accurate. We provide a simulation of the secret key rate versus distance with different parameters. In addition, the minimal detection efficiency required at each distance, as well as the contrast between the two methods, are also shown, so as to provide a reference in terms of system realization.
In continuous-variable quantum key distribution (CV-QKD), the key information are encoded on quadratures of the optical field, which are measured via balanced homodyne detector (BHD). The bandwidth of the BHD is one of key parameters for precise characterization of quantum states. We establish a theoretical model to analyze the impact of the BHD bandwidth and signal modulation patterns on the channel parameters estimation of CV-QKD systems. Based on the proposed model, the secure key rate of a practical CV-QKD system under different BHD bandwidths and signal modulation patterns are investigated. Our results show that insufficient BHD bandwidth will result in wrong estimate of the transmission loss and excess noise, which significantly affects the performance of CV-QKD systems. Given the BHD bandwidth, there exists an optimal signal repetition rate that maximizes the secure key rate. The BHD bandwidth requirement of the QKD system increases with the transmission distance for large duty cycle pulse. Furthermore, the root raised-cosine pulse signal modulation performs better than the square pulse signal modulation in general.
In continuous-variable (CV) QKD with optical coherent detection, the widely adopted trusted detector noise model improves both the secret key rate and the transmission distance. This model assumes that detector noise is inherently random and inaccessible to an adversary. While substantial research has focused on shielding the detector, it is far more difficult to justify the adversary's ignorance of the detector noise. In this paper, we introduce a calibrated detector noise model for CV-QKD, which relies solely on the isolation of the detector from the adversary's intervention. Specifically, our model applies even when detector noise is predictable to the adversary. We analyze the electrical noise of a commercial balanced photoreceiver and perform numerical simulations to compare different noise models. Our results show that when the detector noise variance is an order of magnitude below the vacuum noise, the proposed model achieves a secret key rate comparable to that of the trusted detector noise model, while eliminating the questionable assumption of ``truly random'' detector noise.