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Optics Express

Security analysis of discretized polar modulation continuous-variable quantum key distribution

Tianyi Wang, Ming Li, Xu Wang

Published Sep 9, 2022• 9 citations
Publisher

Abstract

In experimental setups of Gaussian modulation continuous-variable quantum key distribution (CV-QKD), the amplitude and phase of coherent states will be modulated and discretized due to the finite resolution of voltages that drive electro-optical modulators, resulting in Gaussian modulation discretization. We demonstrate that the impact of discretization on CV-QKD can be described as a multiplicative coefficient experimentally and modeled as a preparation noise imposed on ideal Gaussian modulation theoretically. To obtain an accurate estimation of quadrature fluctuation induced by discretized polar modulation, a data-filtering process named preselection can be applied before state transmission. Numerical results show that when amplitude resolution is 0.25 and phase resolution is 0.02, discretized polar modulation enables a transmission distance of 69 km under homodyne detection, reaching 89% of ideal Gaussian modulation. As for heterodyne detection, 55 km and 80% are achieved.

DOI
10.1364/oe.467448

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In experimental setups of Gaussian modulation continuous-variable quantum key distribution (CV-QKD), the amplitude and phase of coherent states will be modulated and discretized due to the finite resolution of voltages that drive electro-optical modulators, resulting in Gaussian modulation discretization. We demonstrate that the impact of discretization on CV-QKD can be described as a multiplicative coefficient experimentally and modeled as a preparation noise imposed on ideal Gaussian modulation theoretically. To obtain an accurate estimation of quadrature fluctuation induced by discretized polar modulation, a data-filtering process named preselection can be applied before state transmission. Numerical results show that when amplitude resolution is 0.25 and phase resolution is 0.02, discretized polar modulation enables a transmission distance of 69 km under homodyne detection, reaching 89% of ideal Gaussian modulation. As for heterodyne detection, 55 km and 80% are achieved.
In experimental setups of continuous-variable quantum key distribution (CV-QKD), the ideal Gaussian modulation will suffer from discretization and degrade into discretized polar modulation (DPM), which deteriorates the accuracy of parameter estimation and results in an overestimation of excess noise. We demonstrate that in the asymptotic case, the DPM-induced estimation bias is determined exclusively by the modulation resolutions and can be modeled as a quadratic function. To obtain an accurate estimation, a calibration on the estimated excess noise is implemented based on the closed-form expression of the quadratic bias model, while statistical analysis of the model residuals defines the upper bound of estimated excess noise and the lower bound of secret key rate. Simulation results show that when modulation variance is 25 and excess noise is 0.02, the proposed calibration scheme can eliminate an estimation bias of 14.5%, thus enhancing the efficiency and feasibility of DPM CV-QKD.
In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced on the receiver side. Implemented by linear optical elements, heterodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combination of the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the composable secret key rate and transmission distance are closely related to the tuning gain and the transmittance of LOCM. Once these two parameters are set to appropriate values, LOCM can improve the secret key rate and transmission distance of DPM-CVQKD, as well as its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, the LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Owing to the fact that the performance of LOCM DPM-CVQKD is largely reliant on the calibration selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be utilized.
In experimental setups of continuous-variable quantum key distribution (CVQKD) independently modulating the amplitude and phase of coherent states, the ideal Gaussian modulation will be degraded into discretized polar modulation (DPM) due to the finite resolution of the driving voltages of electro-optical modulators. To compensate for the performance degradation induced by the joint effect of amplitude and phase discretization, linear optics cloning machine (LOCM) can be introduced at the receiver side to reduce the impact of channel excess noise. Implemented by linear optical elements, homodyne detection and controlled displacement, LOCM introduces extra noise that can be transformed into an advantageous one to combat channel excess noise by dynamically adjusting the relevant parameters into a suitable range. In this paper, the prepare-and-measure version of LOCM DPM-CVQKD is presented, where the incoming signal state enters a tunable LOCM before being measured by the nonideal heterodyne detector. The equivalent entanglement-based model is also established to perform security analysis, where the LOCM is reformulated into combining the incoming signal state and a thermal state on a beam splitter. The composable secret key rate is derived to investigate the security of LOCM DPM-CVQKD. Simulation results demonstrate that the secret key rate is closely related to the tuning gain and the transmittance of LOCM. Once the two parameters are set to appropriate values, LOCM allows the promotion of the secret key rate of DPM-CVQKD, as well as its resistance to excess noise. Meanwhile, taking finite-size effect into consideration, LOCM can also effectively reduce the requirement for the block size of the exchanged signals, which is beneficial to the feasibility and practicability of CVQKD. Since the performance of LOCM DPM-CVQKD is heavily reliant on the calibrate selection of relevant parameters, further research may concentrate on the optimization of LOCM in experimental implementations, where machine learning related methods may be exploited.
Abstract Unidimensional continuous variable quantum key distribution (UD-CVQKD) applies Gaussian modulation on one single quadrature of the coherent state. However, in practical experimentations, the finite resolution of modulator driving voltages will result in Gaussian modulation discretization. To investigate its impact on the security of UD-CVQKD, the discretization of amplitude modulation is modeled and analyzed, with the secret key rate formulated against entangling cloner attack. Simulation results demonstrate that despite the performance degradation, UD-CVQKD protocol with discretized amplitude modulation may relax the restriction on correlation parameters to extend the secure region under certain parameters, which can be beneficial to the practicability of UD-CVQKD.
The major drawbacks of current CV-QKD systems are the achievable secret key rate or transmission distance. Moreover, most of the CV-QKD systems are based on homodyne detection and use a remotely transmitted local oscillator in time or polarization multiplex. This enhances the complexity of the transmitter and the receiver, limits the transmission distance and leaves a security loophole for a potential eavesdropper performing for example a local oscillator calibration attack. In this article, a CV-QKD system using a discrete 8-state phase modulation and a symbol rate of 1 GBd as well as a heterodyne detection with a real local oscillator is experimentally demonstrated. The excess noise, a crucial parameter limiting the achievable key rate and transmission distance, is studied.
We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.