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Laser Physics Letters

Imperfect basis choice in continuous-variable quantum key distribution

Weiqi Liu, Jinye Peng, Jin Qi, Zhengwen Cao, Chen He

Published Apr 16, 2020• 6 citations
Publisher

Abstract

Abstract In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD), basis choice is a necessary procedure if homodyne detector is used. However, finite bandwidth of the digital-to-analog convertor (DAC) at the receiver’s side may lead to the imperfection of the basis choice, namely, maybe Bob can not exactly modulate 0 or π 2 on the phase modulator to implement the homodyne detection.We investigate the GMCS QKD scheme with imperfect basis choice under realistic conditions of quantum channel and detector.We show that the imperfection causes a misestimate of the transmittance and the excess noise, the secret key rate and the security of the system are dramatically decreased consequently. To achieve a reliable quantum key distribution, a security bound to the noise induced by the imperfect basis choice is derived for reverse reconciliation and homodyne detector. Besides, we propose and demonstrate a countermeasure against the noise due to imperfect basis choice.

DOI
10.1088/1612-202x/ab7eb7

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Abstract In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD), basis choice is a necessary procedure if homodyne detector is used. However, finite bandwidth of the digital-to-analog convertor (DAC) at the receiver’s side may lead to the imperfection of the basis choice, namely, maybe Bob can not exactly modulate 0 or π 2 on the phase modulator to implement the homodyne detection.We investigate the GMCS QKD scheme with imperfect basis choice under realistic conditions of quantum channel and detector.We show that the imperfection causes a misestimate of the transmittance and the excess noise, the secret key rate and the security of the system are dramatically decreased consequently. To achieve a reliable quantum key distribution, a security bound to the noise induced by the imperfect basis choice is derived for reverse reconciliation and homodyne detector. Besides, we propose and demonstrate a countermeasure against the noise due to imperfect basis choice.
Measurement basis choice is an essential step in the underwater continuous variable quantum key distribution system based on homodyne detection. However, in practice, finite bandwidth of analog-to-digital converter on the receiver’s side is limited, which can result in defects in the measurement basis choice. That is, the receiver cannot accurately modulate the corresponding phase angle on the phase modulator for measurement basis choice to implement homodyne detection. The imperfect measurement basis choice will introduce extra excess noise, which affects the security of underwater continuous variable quantum key distribution scheme. To solve this problem, we propose an underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice, and analyze the influence of imperfect measurement basis choice on the performance of underwater continuous variable quantum key distribution system in detail. The research results indicate that the extra excess noise introduced by imperfect measurement basis choice can reduce the secret key rate and maximum transmission distance of the underwater Gaussian modulated quantum key distribution, thus reducing the security of the system. In order to achieve reliable underwater continuous variable quantum key distribution, we quantitatively analyze the extra excess noise introduced by choosing the imperfect measurement basis and obtain its security limit. Besides, we also consider the influence of different seawater depths on the security limit of the proposed scheme, effectively solving the security risks caused by the imperfect measurement basis choice. Furthermore, for the proposed scheme, we consider not only its asymptotic security case but also its composable security case, and the performance curves obtained in the latter are tighter than that achieved in the former. The proposed scheme aims to promote the practical process of underwater continuous variable quantum key distribution system and provide theoretical guidance for accurately evaluating the water channel parameters in underwater communication of global quantum communication networks.
In continuous-variable quantum key distribution, the loss and excess noise of the quantum channel are key parameters that determine the secure key rate and the maximal distribution distance. We investigate the imperfect quantum state preparation in Gaussian modulation coherent-state protocol both theoretically and experimentally. We show that the Gaussian distribution characteristic of the prepared states in phase space is broken due to the incorrect calibration of the working parameters for the amplitude modulator and phase modulator. This further causes a significant increase of the excess noise and misestimate of the channel loss. To ensure an accurate estimate of the quantum channel parameters and achieve a reliable quantum key distribution, we propose and demonstrate two effective schemes to calibrate the working parameters of the modulators.
Quantum key distribution (QKD) systems based on the modulation of weak-coherent states and homodyne detection has attracted much attention over last years due to its compatibility with existing telecom equipment. The coherent state required by most of the practical protocols for continuous-variable QKD can be produced in practice using a typical laser source followed by standard phase and amplitude optical modulators. On the other hand, the homodyne detector used to measure the quadratures of the modulated light field can be implemented with high-efficient PIN photodiodes. Moreover, in continuous-variable QKD systems the security of the secret key depends on the precise estimation by Bob of the loss and excess noise of the quantum channel. In this work we discuss the impact of imperfect state preparation by Alice and the role of homodyne detector imbalance on the performance of a continuous-variable QKD system. More specifically, we will consider that Alice phase and amplitude modulators are not ideal suffering from incorrect modulation calibration and optical imbalance, and that the positive and negative currents of Bob homodyne detector are not completely canceled due to a non-ideal beam-splitter and due to different quantum efficiencies of its two photodiodes.
The continuous-variable quantum key distribution (CVQKD) has been demonstrated to be available in practical secure quantum cryptography. However, its performance is restricted strongly by the channel excess noise and the reconciliation efficiency. In this paper, we present a quantum key distribution (QKD) protocol by encoding the secret keys on the random choices of two measurement bases: the conjugate quadratures XXX and PPP. The employed encoding method can dramatically weaken the effects of channel excess noise and reconciliation efficiency on the performance of the QKD protocol. Subsequently, the proposed scheme exhibits the capability to tolerate much higher excess noise and enables us to reach a much longer secure transmission distance even at lower reconciliation efficiency. The proposal can work alternatively to strengthen significantly the performance of the known Gaussian-modulated CVQKD protocol and serve as a multiplier for practical secure quantum cryptography with continuous variables.
We discuss the excess noise contributions of a practical balanced homodyne detector (BHD) in Gaussian-modulated coherent-state (GMCS) quantum key distribution (QKD). We point out that the key generated from the original realistic model of GMCS QKD may not be secure. In our refined realistic model , we take into account excess noise due to the finite bandwidth of the homodyne detector and the fluctuation of the local oscillator (LO). A high-speed BHD suitable for GMCS QKD in the telecommunication wavelength region is built and experimentally tested. The 3 dB bandwidth of the BHD is found to be 104 MHz and its electronic noise level is 13 dB below the shot noise at an LO level of 8.5 × 10 8 photons per pulse. The secure key rate of a GMCS QKD experiment with this homodyne detector is expected to reach Mbits s −1 over a few kilometers.
Continuous-variable quantum key distribution with coherent detection is widely acknowledged for its compatibility with contemporary optical communication technologies. However, the robustness of various modulation formats and detection procedures against high excess noise remains uncertain, posing a significant barrier to the widespread implementation of quantum key distribution networks. This paper introduces a Matlab and Simulink-based experimental simulator designed to analyze different modulation formats (Gaussian and discrete) and coherent detection techniques (homodyne, heterodyne, and intradyne). Our findings suggest that polarization-multiplexed quantum signals with discrete modulation and pilot tones exhibit greater resilience to experimental imperfections. Enhanced robustness can be achieved through post-selection. Furthermore, under conditions of trusted detector noise, intradyne detection proves more effective in mitigating various offsets between the two nodes, thereby resulting in an increased secret key rate. The secure key rate is determined using the Gaussian extremity theorem for Gaussian modulation and a strict numerical technique against collective attacks in the asymptotic regime for discrete modulation. The results demonstrate that the protocol enables key distribution over distances approaching intercity scales, thereby supporting the advancement of cost-effective quantum-secure communication networks.