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arXiv:2107.01798 · Optics Express

Strengthening practical continuous-variable quantum key distribution against measurement angular error

Tao Shen, Yundi Huang, Xiangyu Wang, Huiping Tian, Ziyang Chen, Song Yu

Published Sep 3, 2021• 8 citations
arXivHTMLPDF

Abstract

The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems with heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of 90 ∘ . However, the optical phase shifter in practice introduces imperfections, mainly the measurement angular error, which inevitably deteriorates the security of the practical systems. Here, we will give a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Subsequently, from the parameter estimation, we deduce the overestimated excess noise and the underestimated transmittance, which lead to a reduction in the final secret key rate. Simultaneously, we propose an estimation method of the measurement angular error. Next, the practical security analysis is provided in detail, and the effect of the measurement angular error and its corresponding compensation scheme are demonstrated. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems.

DOI
10.1364/oe.433576

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The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems with heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of 90 ∘ . However, the optical phase shifter in practice introduces imperfections, mainly the measurement angular error, which inevitably deteriorates the security of the practical systems. Here, we will give a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Subsequently, from the parameter estimation, we deduce the overestimated excess noise and the underestimated transmittance, which lead to a reduction in the final secret key rate. Simultaneously, we propose an estimation method of the measurement angular error. Next, the practical security analysis is provided in detail, and the effect of the measurement angular error and its corresponding compensation scheme are demonstrated. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems.
Thermal-state continuous-variable quantum key distribution (CV-QKD) of direct reconciliation with heterodyne detection can improve the robustness of the protocols. However, CV-QKD protocols require outlier detection, optical phase shifters are used to achieve orthogonal differentiation of the modes, but the actual optical phase shifters suffer from measurement angular errors, resulting in the imperfect phase. This kind of error degrades the security of the system. In this paper, we analyze the causes of measurement angular error and its impact on the secret key rate of the thermal-state CV-QKD protocols. We propose a compensation method to compensate for the effects of the measurement angular error and give a more complete secure analysis method under collective attack. The results obtained in this paper further improve the secure analysis under the thermal-state protocol and further enhance the performance of the system using the compensation method.
The value of residual phase noise, after phase compensation, is one of the key limitations of performance improvement for continuous-variable quantum key distribution using a local local oscillator (LLO CV-QKD) system, since it is the major excess noise. However, due to the nonideality of the realistic devices implemented in practice, for example, imperfect lasers, detectors, and unbalanced interferometers, the value of residual phase noise in the current system is still relatively large. Here, we develop a phase noise model to improve the phase noise tolerance of the LLO CV-QKD schemes. In our model, part of the phase-reference measurement noise associated with detection efficiency and electronic noise of Bob's detector as well as a real-time monitored phase-reference intensity at Bob's side is considered trusted because it can be locally calibrated by Bob. We show that using our phase noise model can significantly improve the secure key rate and transmission distance of the LLO CV-QKD system. We further conduct an experiment to substantiate the superiority of the phase noise model. Based on experimental data of a LLO CV-QKD system in the 25-km optical fiber channel, we demonstrate that the secure key rate under our phase noise model is approximately 40% higher than that under the conventional phase noise model.
Continuous variable-quantum key distribution (CV-QKD) based on coherent detection has potential to be a cost-effective solution to deploy secure keys over optical networks. This is due to its compatibility with mature optical communication technologies, such as homodyne and heterodyne detection schemes. Nevertheless, realistic implementations of CV-QKD systems suffer from imperfections in the practical devices used to generate and detect the coherent states. Those imperfections deteriorate the performance of the CV-QKD system and can be exploited by an eavesdropper to steal key information without being detected. In this work, we discuss the impact of practical device imperfections on the excess noise of the CV-QKD and on the achievable transmission distance. We also analyze the impact of detection imperfections on the measurement of the shot noise, and its impact on CV-QKD system security.
Continuous-variable quantum key distribution (CVQKD) with a real local oscillator (LO) is confronted with new security issues attributed to the reference pulses transmitted together with quantum signals over the insecure quantum channel. This paper proposes a method of phase attack on reference pulses of the CVQKD with real LOs. Under the phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers so that the phase compensation error is increased. Consequently, the secret key rate is reduced because of the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, both the parameters of actual transmittance and actual excess noise are deduced from the phase compensation accuracy, and then they are compared with those estimated by training signals. The simulation results show that the secret key rate calculated from the theoretical parameters is consistent with the one estimated by training signals.
In continuous-variable quantum key distribution with a local local oscillator (LLO CV-QKD), the phase noise after phase compensation is mainly composed of three parts: the relative phase drift noise, the relative phase accumulated noise, and the phase-reference measurement noise. Here, we develop a practical phase noise model for LLO CV-QKD protocols, in which part of the phase-reference measurement noise that can be locally calibrated by Bob at the receiver side is considered to be trusted noise. It is reasonable to adopt this model because Bob”s apparatus is inaccessible to the eavesdropper. We show that the secret key rate and the transmission distance of the LLO CV-QKD system under the practical phase noise model is significantly improved in comparison to that under the conventional phase noise model. We show that the secret key rate is improved more than 65% and the transmission distance is increased more than 70% with some typical simulation parameters.
In order to ensure the security of the local oscillator (LO) in continuous variable quantum key distribution (CV-QKD), the LO in CV-QKD based on the local LO (LLO) scheme no longer passes through the quantum channel. For the LLO scheme using homodyne detection, two orthogonal quadratures of reference pulse can only be measured sequentially, which, as a result, each signal pulse should be accompanied by a pair of identical reference pulses. However, due to the phase shift between two adjacent pulses, it is difficult to prepare dual reference pulses with the same phase relative to the LO. In this paper, we propose an improved method to get around this difficulty, which is demonstrated experimentally for a transmitter and a receiver connected by a 50 km single mode fiber. The phase noise measured in the experiment is 2.0×10−3rad2, which is comparable to the recent experimental results using heterodyne detection. This method simplifies the preparation of phase reference pulses and removes the obstacles for the application of homodyne detection in the LLO scheme. In addition, this method can also be used for the compensation of quadrature imbalance in heterodyne detection, then the performance of heterodyne detection can be improved.