As a core component of the continuous variable quantum secret sharing system, the performance of the detector is crucial to the entire system. Nevertheless, in practical circumstances, the detector is nonideal, whose defects can introduce noise interference into the signal and result in the performance degradation of the continuous-variable quantum secret sharing system. To solve this problem, we present a Gaussian-modulated continuous-variable quantum secret sharing based on phase-insensitive amplifiers. The phase-insensitive amplifier can uniformly amplify each orthogonal component of the signal and increase the signal power, thereby relatively reducing the noise interference caused by the defects of nonideal detectors to the signal and significantly improving the actual performance of the system. The numerical simulation shows that the phase-insensitive amplifier effectively increases the secret key rate and the secure transmission distance of the system, and the actual performance of the system under the high gain of the phase-insensitive amplifier closely approaches the performance of the system using an ideal detector. This work provides a novel approach to addressing the issue of reduced performance of continuous-variable quantum secret sharing caused by the defects of nonideal detectors.
As a core component of the continuous variable quantum secret sharing system, the performance of the detector is crucial to the entire system. Nevertheless, in practical circumstances, the detector is nonideal, whose defects can introduce noise interference into the signal and result in the performance degradation of the continuous-variable quantum secret sharing system. To solve this problem, we present a Gaussian-modulated continuous-variable quantum secret sharing based on phase-insensitive amplifiers. The phase-insensitive amplifier can uniformly amplify each orthogonal component of the signal and increase the signal power, thereby relatively reducing the noise interference caused by the defects of nonideal detectors to the signal and significantly improving the actual performance of the system. The numerical simulation shows that the phase-insensitive amplifier effectively increases the secret key rate and the secure transmission distance of the system, and the actual performance of the system under the high gain of the phase-insensitive amplifier closely approaches the performance of the system using an ideal detector. This work provides a novel approach to addressing the issue of reduced performance of continuous-variable quantum secret sharing caused by the defects of nonideal detectors.
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.
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.
In practical quantum communication networks, the scheme of continuous-variable quantum key distribution (CVQKD) faces a challenge that the entangled source is controlled by a malicious eavesdropper, and although it still can generate a positive key rate and security, its performance needs to be improved, especially in secret key rate and maximum transmission distance. In this paper, we proposed a method based on the four-state discrete modulation and a heralded hybrid linear amplifier to enhance the performance of CVQKD where the entangled source originates from malicious eavesdropper. The four-state CVQKD encodes information by nonorthogonal coherent states in phase space. It has better transmission distance than Gaussian modulation counterpart, especially at low signal-to-noise ratio (SNR). Moreover, the hybrid linear amplifier concatenates a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), which can improve the probability of amplification success and reduce the noise penalty caused by the measurement. Furthermore, the hybrid linear amplifier can raise the SNR of CVQKD and tune between two types of performance for high-gain mode and high noise-reduction mode, therefore it can extend the maximal transmission distance while the entangled source is untrusted.
Abstract Inherent defects of the detectors in a practical system cause deterioration of the performance of the unidimensional coherent-state continuous-variable quantum key distribution protocol. Aiming to achieve optimal performance, we propose a method of using a phase-sensitive amplifier to overcome the limitation that the detectors introduce. The modified protocol, corresponding to a higher key rate, provides the practical system with more robustness. To conduct a thorough investigation into the effects that the phase-sensitive amplifier creates, the expressions of the secret key rates are derived, under the conditions of coherent states, homodyne detection against collective attacks, and a phase-sensitive optical amplifier added at the output of the channel. Then, we carry out simulations to observe the performance in the cases of different gains. The simulation results demonstrate that the method we propose can improve the performance of the unidimensional protocol using coherent states and make up for the imperfections of the detector in a practical system.
Continuous-variable quantum secret sharing (CVQSS) enables multiple players (at least three) to share a secret key using weak coherent states, which are easy to prepare and resilient to losses. Despite these advantages, CVQSS encounters challenges such as low secret key rates and limited maximum transmission distances, particularly when dealing with a large number of players. This paper proposes a novel scheme to enhance CVQSS performance by incorporating a heralded hybrid linear amplifier (HHLA). The HHLA combines a deterministic linear amplifier (DLA) and a noiseless linear amplifier (NLA), effectively functioning as an improved noiseless linear amplifier with a higher probability of successful amplification. Additionally, the HHLA offers tunable gain settings, including a high-gain mode and a high noise-reduction mode, to optimize noise penalties form measurements and enhance CVQSS performance. Numerical simulations demonstrate that even with 100 connected nodes, the HHLA-based CVQSS scheme achieves a maximum transmission distance exceeding 60 km.
Abstract We propose a method to improve transmission distance of continuous-variable quantum key distribution via a heralded hybrid linear amplifier (HLA), involving an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The phase-insensitive amplification of quantum light states may experience a degradation of signal-to-noise ratio (SNR) of 3dB which can be surmounted by the probabilistic amplification process. The new hybrid amplifier allows one to tune between the regimes of high gain or high noise reduction and control the trade-off between the amplification coefficient and a finite heralding probability flexibly. Our equipment could clone unknown coherent states with fidelity surpassing the no-cloning limit by abandoning determinism and using probabilistic methods. The setup has a better compatibility with continuous variable protocols as it only uses Gaussian elements and a post-selection algorithm. The hybrid linear amplifier enhances the SNR and hence the transmission distance of the CVQKD protocol is extended. Both the asymptotic secret key rate and the secret key rate in a finite-size scenario are analyzed in this paper.