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.
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) offers significant potential for long-distance secure communication, benefiting from its quadratic scaling capacity and phase compensation-free characteristic. However, MP-QKD still requires stringent wavelength consistency between remote lasers, which is impractical with commercial lasers without locking. In this work, we develop a simple optical-frequency-comb-based MP-QKD system to simultaneously establish coherence and distribute keys with free-running commercial lasers. We implement the experiment over standard single-mode fiber with a loss coefficient of 0.2 dB/km. The system achieves finite-size secret key rates (SKRs) of 561.26, 113.59, and 10.20 bits per second over 303.37, 354.62, and 404.25 km, which are 1.0267, 2.5230, and 2.1033 times of the rate-loss limit. Besides, the SKR over 202.31 km is 8695.34 bits per second, which is sufficient to support practical cryptographic applications. These results validate the practicality and robustness of our method, offering a simplified yet high-performance framework for long-distance secure communication.
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.
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.
Quantum key distribution (QKD) enables information-theoretically secure communication against eavesdropping. However, phase instability remains a challenge across many QKD applications, particularly in schemes such as twin-field QKD and measurement-device-independent QKD. The most dominant source of phase fluctuation arises from the frequency offset between independent lasers. Here we propose a method to address this issue by employing a classical photodiode to compensate for the laser frequency difference. As an application of this method, we implement this technique in a mode-pairing QKD system, achieving an error rate approaching the theoretical limit and surpassing the linear key-rate bound over a fiber distance of 296.8 km. This approach provides a practical solution for frequency matching between independent lasers and can be extended to other fields requiring precise phase stabilization.
Abstract Mode-pairing quantum key distribution (MP-QKD) is a potential protocol that is not only immune to all possible detector side channel attacks, but also breaks the repeaterless rate-transmittance bound without needing global phase locking. Here we analyze the finite-key effect for the MP-QKD protocol with rigorous security proof against general attacks. Moreover, we propose a six-state MP-QKD protocol and analyze its finite-key effect. The results show that the original protocol can break the repeaterless rate-transmittance bound with a typical finite number of pulses in practice. And our six-state protocol can improve the secret key rate significantly in long distance cases.
Quantum communications promise to provide information theoretic security in the exchange of information. However, unlike their classical counterpart, they utilise dim optical pulses whose amplification is prohibited. Consequently, their transmission rate and range is confined below a theoretical limit known as repeaterless secret key capacity. Overcoming this limit with today’s technology was believed to be impossible until the recent proposal of Twin-field (TF) quantum key distribution (QKD), a scheme that uses phase-coherent optical signals and an auxiliary measuring station to distribute quantum information. Here, TF-QKD and its main variations are initially explored and compared in simulations, to assess their performance in different attributes. Such schemes are also practically implemented for the first time in two experiments. The first is a proof-of-principle implementation over significant channel losses, in excess of 90 dB. In the second, the setup is developed further and the protocol is implemented over real fibre channels exceeding 600 km in length, representing the first fibre-based secure quantum communication beyond the barriers of 600 km and 100 dB. In both cases, in the high loss/distance regime, the resulting secure key rates exceed the repeaterless secret key capacity, a result never achieved before.