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Acta Physica Sinica

Underwater continuous variable quantum key distribution scheme based on imperfect measurement basis choice

Xiao-Dong Wu, Duan Huang

Published Jan 1, 2024• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.73.20240804

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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.
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.
In a practical quantum communication system, the security of signal source of continuous-variable quantum key distribution may be jeopardized due to device flaws and hidden attacks. In this paper, an improved scheme for Gaussian-modulated continuous-variable quantum key distribution based on an untrusted entangled source is proposed. In particular, the entanglement source is placed in an untrusted quantum channel to simulate that it is controlled by an eavesdropper, thereby verifying the security of Gaussian-modulated continuous-variable quantum key distribution in a complex environment. This work in detail analyzes the influence of untrusted entanglement source on practical Gaussian-modulated continuous-variable quantum key distribution system, and the numerical simulation shows that the performance of Gaussian-modulated continuous-variable quantum key distribution will dramatically decrease once the entanglement source has moved out of the sender, and it will slightly rise as the untrusted entanglement source slowly moves away from the sender. This paper further introduces two kinds of optical amplifiers, which are phase-sensitive amplifier and phase-insensitive amplifier, to compensate for the imperfection of the coherent detector. These amplifiers are beneficial to enhancing the quantum efficiency of the receiver’s detector. Specifically, the security key rate of Gaussian-modulated continuous-variable quantum key distribution with homodyne detection can be well improved by phase-sensitive amplifier, and the security key rate of Gaussian-modulated continuous-variable quantum key distribution with heterodyne detection can be well improved by phase-insensitive amplifier. To summary, this paper proposes a scheme for Gaussian-modulated continuous-variable quantum key distribution with untrusted entanglement source, experimental results show that the proposed scheme can generate secure quantum keys even if the Gaussian entanglement source is untrusted, and the two optical amplifiers can effectively improve the quantum efficiency of the detector at the receiver. This work aims to promote the practical process of the Gaussian-modulated continuous-variable quantum key distribution system and provide theoretical guidance for the practical implementation and application of the Gaussian-modulated continuous-variable quantum key distribution system.
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.
Gaussian-modulated coherent state quantum key distribution is gradually moving towards practical application. Generally, the involved scheme is based on the binary random basis choice. To improve the performance and security, we present a scheme based on a continuous random basis choice. The results show that our scheme obviously improves the performance, such as the secure communication distance. Our scheme avoids comparing the measurement basis and discarding the key bits, and it can be easily implemented with current technology. Moreover, the imperfection of the basis choice can be well removed by the known phase compensation algorithm.
We investigate the optical absorption and scattering properties of four different kinds of seawater as the quantum channel. The models of discrete-modulated continuous-variable quantum key distribution (CV-QKD) in free-space seawater channel are briefly described, and the performance of the four-state protocol and the eight-state protocol in asymptotic and finite-size cases is analyzed in detail. Simulation results illustrate that the more complex is the seawater composition, the worse is the performance of the protocol. For different types of seawater channels, we can improve the performance of the protocol by selecting different optimal modulation variances and controlling the extra noise on the channel. Besides, we can find that the performance of the eight-state protocol is better than that of the four-state protocol, and there is little difference between homodyne detection and heterodyne detection. Although the secret key rate of the protocol that we propose is still relatively low and the maximum transmission distance is only a few hundred meters, the research on CV-QKD over the seawater channel is of great significance, which provides a new idea for the construction of global secure communication network.
Continuous variable quantum secret sharing protocol can guarantee the unconditional security of secret key information based on the fundamental laws of physics. However, the state preparation operation may become non-ideal and imperfect in practical continuous variable quantum secret sharing scheme, which will introduce additional excess noise and affect the security of the scheme. Therefore, it is necessary to analyze it. We propose a practical continuous variable quantum secret sharing protocol based on imperfect state preparation. Specifically, in the proposed scheme, we assume that there are multiple users, and the imperfect state preparation performed by any user is equivalent to the corresponding untrusted third party using a phase insensitive amplifier to amplify the ideal modulator and laser owned by the user. The equivalent excess noise introduced by the imperfect state preparation can be calculated comprehensively and quantitatively through the gain of the corresponding phase insensitive amplifier. The results show that the continuous variable quantum secret sharing scheme is sensitive to the excess noise introduced by the imperfect state preparation operation, which will inevitably reduce its performance and security. Fortunately, the upper bound of the additional excess noise tolerance for the imperfect state preparation is achieved by using the specific gain formula of the phase insensitive amplifier, thus the security risks caused by the imperfect state preparation can be effectively solved. Due to considering the additional excess noise introduced by imperfect state preparation, tighter secret key rate curves can be obtained by the proposed scheme than those by the ideal continuous variable quantum secret sharing protocol. These results indicate that the proposed scheme can improve the practical security of continuous variable quantum secret sharing scheme, and provide a theoretical basis for its practical applications.