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Previous research has aimed to precisely estimate information leakage to improve the secure key rate (SKR) and maximum transmission distance in quantum key distribution (QKD). However, existing methods repeatedly considerd the information of the multi-photon pulses known to Eve before and after information reconciliation, resulting in an overestimation of the leakage amount. We propose a novel approach that considers the quantum part's effect on post-processing, providing a more accurate estimation of information reconciliation leakage to improve the SKR. Theoretical analysis shows that our method more accurately estimates the information reconciliation leakage, significantly improving the SKR at any distance as well as the maximum transmission distance. It is worth mentioning that previous studies treat information leakage of the error correction as Shannon bound $Nh(e)$, and our method can estimate it more tightly. Simulation results for decoy-BB84 and measurement-device-independent (MDI) protocols using Cascade are consistent with the theoretical analysis. The farther the transmission distance, the greater the growth rate of SKR. When the error rate is 33%, compared with the original method, the SKR growth rate of decoy-BB84 at 100KM is 100.4%, and the transmission distance of MDI increases by 22KM.

Quantum key distribution (QKD) is an important branch of quantum information science as it holds promise for unconditionally secure communication. For QKD research, a central issue is to improve the final secure key rate (SKR) and the maximal transmission distance. To address this issue, most works focused on reducing the information leakage of QKD. In this paper, we propose a novel approach to further reduce the information leakage by specially considering the overlap between the information leakage of quantum part and post-processing part. The overlap means that the information leakage of post-processing part caused solely by multi-photon pulses is considered twice in previous studies, i.e., both in quantum part and post-processing part. Since the information carried by multi-photon pulses has been considered as completely known by Eve through the photon-number-splitting attack in quantum part, there is no need to consider it in post-processing part repetitively during the SKR calculation. Therefore, our approach can theoretically reduce the information leakage of a QKD protocol. Based on this idea, we derive the formulas to calculate the amount of information leakage for decoy-BB84 and sending-or-not-sending twin-field protocols. Simulation results for these two typical protocols also demonstrate that our approach evidently improves the SKR as well as the maximal transmission distance under practical experimental parameters., Comment: 9 pages, 3 figures

Twin-Field quantum key distribution (TF-QKD) and its variants, e.g. Phase-Matching QKD, Sending-or-not-sending QKD, and No Phase Post-Selection TFQKD promise high key rates at long distance to beat the rate distance limit without a repeater. The security proof of these protocols are based on decoy-state method, which is usually performed by actively modulating a variable optical attenuator together with a random number generator in practical experiments, however, active-decoy schemes like this may lead to side channel and could open a security loophole. To enhance the source security of TF-QKD, in this paper, we propose passive-decoy based TF-QKD, in which we combine TF-QKD with the passive-decoy method. And we present a simulation comparing the key generation rate with that in active-decoy, the result shows our scheme performs as good as active decoy TF-QKD, and our scheme could reach satisfactory secret key rates with just a few photon detectors. This shows our work is meaningful in practice.

Quantum key distribution (QKD) can help two distant peers to share secret key bits, whose security is guaranteed by the law of physics. In practice, the secret key rate of a QKD protocol is always lowered with the increasing of channel distance, which severely limits the applications of QKD. Recently, twin-field (TF) QKD has been proposed and intensively studied, since it can beat the rate-distance limit and greatly increase the achievable distance of QKD. Remarkalebly, K. Maeda et. al. proposed a simple finite-key analysis for TF-QKD based on operator dominance condition. Although they showed that their method is sufficient to beat the rate-distance limit, their operator dominance condition is not general, i.e. it can be only applied in three decoy states scenarios, which implies that its key rate cannot be increased by introducing more decoy states, and also cannot reach the asymptotic bound even in case of preparing infinite decoy states and optical pulses. Here, to bridge this gap, we propose an improved finite-key analysis of TF-QKD through devising new operator dominance condition. We show that by adding the number of decoy states, the secret key rate can be furtherly improved and approach the asymptotic bound. Our theory can be directly used in TF-QKD experiment to obtain higher secret key rate. Our results can be directly used in experiments to obtain higher key rates.

Twin-field quantum key distribution (TF-QKD) and its variant protocols are highly attractive due to the advantage of overcoming the rate-loss limit for secret key rates of point-to-point QKD protocols. For variations of TF-QKD, the key point to ensure security is switching randomly between a code mode and a test mode. Among all TF-QKD protocols, their code modes are very different, e.g. modulating continuous phases, modulating only two opposite phases, and sending or not sending signal pulses. Here we show that, by discretizing the number of global phases in the code mode, we can give a unified view on the first two types of TF-QKD protocols, and demonstrate that increasing the number of discrete phases extends the achievable distance, and as a trade-off, lowers the secret key rate at short distances due to the phase post-selection.

Twin-Field Quantum Key Distribution(TF-QKD) protocol and its variants, such as Phase-Matching QKD(PM-QKD), sending or not QKD(SNS-QKD) and No Phase Post-Selection TF-QKD(NPP-TFQKD), are very promising for long-distance applications. However, there are still some gaps between theory and practice in these protocols. Concretely, a finite-key size analysis is still missing, and the intensity fluctuations are not taken into account. To address the finite-key size effect, we first give the key rate of NPP-TFQKD against collective attack in finite-key size region and then prove it can be against coherent attack. To deal with the intensity fluctuations, we present an analytical formula of 4-intensity decoy state NPP-TFQKD and a practical intensity fluctuation model. Finally, through detailed simulations, we show NPP-TFQKD can still keep its superiority of high key rate and long achievable distance., Comment: 16 pages, 9 figures

The parameters choosing (such as probabilities of choosing X-basis or Z-basis, intensity of signal state and decoy state, etc.) and system calibrating will be more challenging when the number of users of a measurement-device-independent quantum key distribution(MDI-QKD) network becomes larger. At present, people usually use optimization algorithms to search the best parameters. This method can find the optimized parameters accurately but may cost lots of time and hardware resources. It's a big problem in large scale MDI-QKD network. Here, we present a new method, using Back Propagation Artificial Neural Network(BPNN) to predict, rather than searching the optimized parameters. Compared with optimization algorithms, our BPNN is faster and more lightweight, it can save system resources. Another big problem brought by large scale MDI-QKD network is system recalibration. BPNN can support this work in real time, and it only needs to use some discarded data generated from communication process, rather than require us to add additional devices or scan the system, Comment: 7 pages, 8 figures