Mode-pairing quantum key distribution (MP-QKD) is advantageous for long-distance secure communication, leveraging its simple implementation and quadratic scaling capacity. The post-measurement pairing in MP-QKD alleviates the photon-coincidence demands, which are essential for surpassing the fundamental limit to the key-rate transmission. In this work, we propose an improved decoy-state MP-QKD protocol featuring a flexible and efficient pairing strategy. We prove the security of the proposed scheme by presenting an entanglement model for decoy-state MP-QKD. The simulation results show that the secret key rate (SKR) can be enhanced among all distances. Notably, compared with the original scheme [Nature Communication13, 3903 (2022)10.1038/s41467-022-31534-7], the improvement of SKR is greater than 65% within 375 km in the asymptotic case and greater than 50% within 400 km in the finite case. And the achievable distance can be extended in the finite case, especially with a small block length. The simulation results demonstrate the high efficiency of the proposed scheme, which is expected to promote the practical applicability of MP-QKD. Furthermore, the entanglement model could provide a theoretical framework for further security and performance analysis of decoy-state MP-QKD.
Mode-pairing quantum key distribution (MP-QKD) is advantageous for long-distance secure communication, leveraging its simple implementation and quadratic scaling capacity. The post-measurement pairing in MP-QKD alleviates the photon-coincidence demands, which are essential for surpassing the fundamental limit to the key-rate transmission. In this work, we propose an improved decoy-state MP-QKD protocol featuring a flexible and efficient pairing strategy. We prove the security of the proposed scheme by presenting an entanglement model for decoy-state MP-QKD. The simulation results show that the secret key rate (SKR) can be enhanced among all distances. Notably, compared with the original scheme [Nature Communication13, 3903 (2022)10.1038/s41467-022-31534-7], the improvement of SKR is greater than 65% within 375 km in the asymptotic case and greater than 50% within 400 km in the finite case. And the achievable distance can be extended in the finite case, especially with a small block length. The simulation results demonstrate the high efficiency of the proposed scheme, which is expected to promote the practical applicability of MP-QKD. Furthermore, the entanglement model could provide a theoretical framework for further security and performance analysis of decoy-state MP-QKD.
Mode-pairing (MP) quantum key distribution (QKD) eliminates the requirements of phase locking and phase tracking compared with twin field (TF) QKD while still surpassing the fundamental rate-distance limit of QKD. The complexity of the experimental implementation is reduced while the efficiency can still be guaranteed. In MP-QKD, two communication parties need to pair two effective rounds according to the announced results by the third party. Therefore it is not intuitive how to provide an entanglement protocol equivalent to the prepare-and-measure protocol for proving security. At present, the security of MP-QKD is rigorously proven by examining the consistency of the states detailly between MP-QKD and the fixed-pairing scheme under all of Eve's possible interference to obtain the equivalence, and verifying the security of the latter. Here, we directly present an entanglement model for MP-QKD by proposing a free-pairing entanglement scheme that is equivalent to MP-QKD. This entanglement model simplifies the security proof and provides a clearer insight into the foundation of MP-QKD. Besides, it could provide a theoretical framework for the comprehensive analysis of MP-QKD, such as facilitating practical security analysis. Additionally, we propose an optimized pairing strategy based on the entanglement model. The simulation results show an enhancement of 163% in pairing efficiency with a reasonable pairing interval 2 × 10 5 .
The mode pairing quantum key distribution (MP-QKD) protocol has attracted considerable attention for its capability to ensure high secure key rates over long distances without requiring global phase locking. However, ensuring symmetric channels for the MP-QKD protocol is challenging in practical quantum communication networks. Previous studies on the asymmetric MP-QKD protocol have relied on ideal decoy state assumptions and infinite-key analysis, which are unattainable for real-world deployment. In this paper, we conduct a security analysis of the asymmetric MP-QKD protocol with the finite-key analysis, where we discard the previously impractical assumptions made in the decoy state method. Combined with statistical fluctuation analysis, we globally optimized the 10 independent parameters in the asymmetric MP-QKD protocol by employing our modified particle swarm optimization. Through further analysis, the simulation results demonstrate that our work achieves improved secure key rates and transmission distances compared to the strategy with additional attenuation. We further investigate the relationship between the intensities and probabilities of signal, decoy, and vacuum states with transmission distance, facilitating their more efficient deployment in future quantum networks.
Mode-pairing quantum key distribution (MP-QKD) can surpass the repeaterless rate-transmittance bound (Pirandola-Laurenza-Ottaviani-Banchi bound) without requiring global phase locking, exhibiting remarkable flexibility. However, MP-QKD necessitates equal communication distances in two channels, which is a challenging requirement in practical applications. To address this limitation, we extend the original MP-QKD to asymmetric cases. Our decoy-state estimation confirms that asymmetric channel transmittances and asymmetric intensities do not compromise the security of the protocol. We focus on the pulse-intensity relationship, a key factor for optimizing the performance of asymmetric MP-QKD. Unlike previous asymmetric protocols, the intensities of different bases in asymmetric MP-QKD cannot be decoupled. We introduce an optimal-pulse-intensity method, adaptable to various scenarios, to enhance key rates by calculating ideal pulse intensities. Simulation results in various representative scenarios indicate that our method effectively reduces the impact of asymmetric channel distances on MP-QKD performance, enhancing its practical applicability.
Abstract A mode-pairing quantum key distribution based on heralded pair-coherent source with passive decoy-states is proposed, named HPCS-PDS-MP-QKD protocol, where the light sources at Alice and Bob sides are changed to heralded pair-coherent sources, and devices designed to implement passive decoy states are included at the transmitter sides to generate the decoy state pulses in the decoy-state window passively. With the defined efficient events and the designed pairing strategy, the key bits and bases can be obtained by data post-processing. Numerical simulation results verify the feasibility of the proposed protocol. The results show that the proposed protocol can exceed PLOB when the pairing interval setting is greater than 103, and the transmission distance exceeds 200 km. When the key transmission distance reaches 300 km and the maximum pairing interval is equivalent to 1, its performance is improved by nearly 1.8 times compared to the original MP-QKD protocol with a weak coherent source (WCS-MP-QKD), and by 6.8 times higher than that of WCS-MP-QKD with passive decoy states (WCS-PDS-MP-QKD). Meanwhile, the key transmission distance can reach 480 km, and surpasses the WCS-PDS-MP-QKD protocol by nearly 40 km. When the total pulse length is greater than 1011, the key generation rate is almost equal to that of infinite pulses. It is a promising QKD protocol that breaks the PLOB bound without requiring phase tracking and locking, has a longer transmission distance and a higher key generation rate, and eliminates the potential of side channel attack.
Quantum key distribution (QKD) provides information-theoretic security for communication. The mode-pairing (MP) protocol emerges as a promising solution for long-distance QKD by eliminating the need for a global phase reference while maintaining the repeaterlike rate-loss scaling. Recent implementations have demonstrated its potential, but they either rely on costly ultrastable lasers or struggle with phase fluctuations from commercial lasers, particularly over long distances. As a result, surpassing the repeaterless bound with a practical system remains a challenge. In this work, we demonstrate a practical high-performance MP-QKD system using commercial lasers. To address phase fluctuations, we propose a frequency-tracking scheme based on fast Fourier transformation, enabling us to extend the pairing length to 2 × 10 5 pulses ( 160 μ s ). We propose a model to carefully analyze the phase noise and optimize the system parameters. Our system achieves an optimal secret key rate of 47.8 bit / s over 403 km of standard fiber (76.5 dB loss), exceeding the repeaterless bound by a factor of 2.92. Furthermore, we compare MP-QKD and twin-field QKD under various practical conditions and clarify the distinct application scenarios of the two protocols. These results confirm the feasibility of MP-QKD using cost-effective commercial technologies, paving the way for scalable quantum communication networks.
Mode-pairing quantum key distribution (MP-QKD) circumvents the need for phase locking through post-selection pairing, still allowing it to surpass the repeaterless rate-transmittance limit. This protocol, therefore, presents a promising approach for practical QKD implementation. Without phase locking and tracking, the performance of the laser, channel, and detector critically affects the determination of the maximum pairing length l in pairing strategies. However, previous studies have typically set l based on empirical data without conducting a thorough analysis. In this study, to more accurately reflect real-world conditions, we consider fiber fluctuations, laser linewidth, laser frequency offset, and after-pulse effect to quantify the systematic misalignment determined by l . We employ the three-intensity decoy-state method, accounting for the finite data-size effect, to evaluate the impact of l in practical scenarios. Our simulation results demonstrate significant enhancements achievable through the optimal selection of l . Therefore, this study provides valuable insights for the advancement of future MP-QKD experiments and applications.