On High-Dimensional Twin-Field Quantum Key Distribution

The twin-field quantum key distribution (TF-QKD) protocol and its variants can overcome the well-known rate-loss bound without quantum repeaters, which have attracted significant attention. Generally, to ensure the security of these protocols, weak coherent states with continuous randomized phases are always assumed in the test mode. However, this assumption is difficult to meet in practice. To bridge the gap between theory and practice, we propose two alternative discrete-phase-randomized (DPR)-twin-field quantum key distribution protocols, which remove the phase sifting procedure in the code mode. Simulation results show that when compared with previous discrete-phase-randomized-twin-field quantum key distribution protocols, our modified protocols can significantly improve the secret key rate in the low channel loss range, which is very promising for practical twin-field quantum key distribution systems.

Quantum key distribution (QKD) enables the establishment of shared keys between two distant users, Alice and Bob, based on the fundamental principles of quantum mechanics, and it has proven to possess information-theoretic security. In most of QKD systems, Alice and Bob require a shared reference frame, and real-time calibration of the reference frame increases system costs and reduces its performance. Fortunately, the reference-frame-independent QKD protocol has been proposed, overcoming reference-frame drift issues and receiving widespread attention. However, in practical QKD systems, the non-ideal characteristics of realistic devices introduce certain inconsistency between the theory and the practice. In real-world quantum key distribution systems, device imperfections can lead to security vulnerabilities, thereby reducing system security. For example, imperfections in the encoding apparatus at the source end may result in errors in the quantum states. The inherent defects in the detection part may cause after-pulse effects and dead-time effects, thus reducing the key rate. Therefore, in this work, we propose a practical state-preparation error tolerant reference-frame-independent quantum key distribution protocol by taking imperfections in both the source and the detectors into account. Moreover, a three-intensity decoy-state scheme for modeling analysis and numerical simulations is employed. In this protocol, we reduce the influence of state-preparation errors on the key rate by utilizing virtual state methods to precisely estimate the phase-error rate. Furthermore, by characterizing the effects of after-pulses and dead-time on the key rate, our protocol exhibits higher robustness and can effectively address issues related to detector imperfections. This approach can also be extended to other quantum key distribution protocols with higher security levels, such as measurement-device-independent quantum key distribution protocol and twin-field quantum key distribution, further mitigating the influence of device imperfections on practical implementation of QKD system. Therefore, our present work provide important reference value for putting the quantum key distributions into practical application.

The sending-or-not-sending (SNS) protocol is one of the most major variants of the twin-field (TF) quantum key distribution (QKD) protocol and has been realized in a 511-km field fiber, the farthest field experiment to date. In practice, however, all decoy-state methods have unavoidable source errors, and the source errors may be non-random, which compromises the security condition of the existing TF-QKD protocols. In this study, we present a general approach for efficiently calculating the SNS protocol's secure key rate with source errors, by establishing the equivalent protocols through virtual attenuation and the tagged model. This makes the first result for TF QKD in practice where source intensity cannot be controlled exactly. Our method can be combined with the two-way classical communication method such as active odd-parity pairing to further improve the key rate. The numerical results show that if the intensity error is within a few percent, the key rate and secure distance only decrease marginally. The key rate of the recent SNS experiment in the 511-km field fiber is still positive using our method presented here, even if there is a [Formula: see text] intensity fluctuation. This shows that the SNS protocol is robust against source errors.

Physical implementations of quantum key distribution (QKD) protocols, like the Bennett-Brassard (BB84), are forced to use attenuated coherent quantum states, because the sources of single photon states are not functional yet for QKD applications. However, when using attenuated coherent states, the relatively high rate of multi-photonic pulses introduces vulnerabilities that can be exploited by the photon number splitting (PNS) attack to brake the quantum key. Some QKD protocols have been developed to be resistant to the PNS attack, like the decoy method, but those define a single photonic gain in the quantum channel. To overcome this limitation, we have developed a new QKD protocol, called ack-QKD, which is resistant to the PNS attack. Even more, it uses attenuated quantum states, but defines two interleaved photonic quantum flows to detect the eavesdropper activity by means of the quantum photonic error gain (QPEG) or the quantum bit error rate (QBER). The physical implementation of the ack-QKD is similar to the well-known BB84 protocol.

Quantum key distribution (QKD) is a cornerstone of secure communication in the quantum era, yet most existing protocols are designed for point-to-point transmission, limiting their scalability in networked environments. In this work, we introduce Loop-Back QKD, a novel QKD protocol that supports both two-party linear configurations and scalable multiuser ring topologies. By leveraging a structured turn-based mechanism and bidirectional pulse propagation, the protocol enables efficient key distribution while reducing the quantum bit error rate (QBER) through a multi-pulse approach. Unlike trusted-node QKD networks, Loop-Back QKD eliminates intermediate-node vulnerabilities, as secret keys are never processed by intermediate nodes. Furthermore, unlike Measurement-Device-Independent (MDI-QKD) and Twin-Field QKD (TF-QKD), which require complex entanglement-based setups, Loop-Back QKD relies solely on direct polarization transformations, reducing vulnerability to side-channel attacks and practical implementation challenges. Additionally, our analysis indicates that multi-pulse Loop-Back QKD can tolerate higher QBER thresholds. However, this increased robustness comes at the cost of a lower key rate efficiency compared to standard QKD schemes. This design choice enhances its robustness against real-world adversarial threats, making it a strong candidate for secure multiuser communication in local and metropolitan-scale quantum networks.

High-dimensional quantum key distribution (QKD) allows achievement of information-theoretic secure communications, providing high key-generation rates, which cannot, in principle, be obtained by QKD protocols with binary encoding. Nonetheless, the amount of experimental resources needed increases as the quantum states to be detected belong to a larger Hilbert space, thus raising the costs of practical high-dimensional systems. Here, we present an alternative scheme for fiber-based four-dimensional QKD, with time and phase encoding and one-decoy state technique. Quantum state transmission is tested over different channel lengths up to 145 km of standard single-mode fiber, evaluating the enhancement of the secret key rate in comparison to the three-state two-dimensional BB84 protocol, which is tested with the same experimental setup. Our scheme allows measurement of the four-dimensional states with a simplified and compact receiver, where only two single-photon detectors are necessary, thus making it a cost-effective solution for practical and fiber-based QKD.

Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step forward toward this direction, with early demonstrations suggesting it can beat the current rate-versus-distance records. A recently introduced variant of TF-QKD is particularly suited for experimental implementation, and has been shown to offer a higher key rate than other variants in the asymptotic regime, where users exchange an infinite number of signals. Here, we extend the security of this protocol to the finite-key regime, showing that it can overcome the fundamental bounds on point-to-point QKD with ~1010 transmitted signals. In many practical regimes of interest, our analysis offers higher key rates than those of alternative variants. Moreover, some of the techniques we develop are applicable to the finite-key analysis of other QKD protocols.

Covert communication methods are used in the communication with high security level. When it turns to quantum communication, covertness is also an important concern which is firstly discussed by Arrazola and Scarani (Phys Rev Lett, 117:250503, 2016). To make quantum key distribution (QKD) protocol more suitable in the scenarios need high security, we propose a covert QKD protocol with decoy-state method in this paper. The secure key rate and covertness of the covert decoy-state QKD are proved. We compare the performance of the covert decoy-state QKD with those of the original decoy-state QKD and covert QKD without decoy states in numerical simulations. It shows that (1) the covert decoy-state QKD can have a performance comparable to the original decoy-state QKD protocol besides its covertness; (2) the covert decoy-state QKD can have a considerable improvement of transmission distance over covert QKD without decoy states at the cost of a small change of covertness parameter. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the Gaussian analysis method.

Quantum key distribution (QKD) is one of the exciting applications of quantum mechanics. It allows the sharing of secret keys between two communicating parties with unconditional security. A variety of QKD protocols have been proposed since the inception of the BB84 protocol. Among different implementation techniques of QKD protocols, there is a category which exploits higher dimensions qubit states to encode classical bits. In this paper, we focus on such a QKD protocol called KXB10, which uses three bases with higher dimensions. Analysis of the generalized dimension quantum states is performed by evaluating it based on the index transmission error rate ITER. We find that there is a direct relationship between qubit dimensions and ITER for the KXB10 protocol.

Chapter 6 - Quantum key distribution

Odd-parity error rejection (OPER), in particular the method of actively odd parity pairing (AOPP), can drastically improve the asymptotic key rate of sending-or-not-sending twin-field (SNS-TF) quantum key distribution (QKD). However, in practice, the finite-key effects have to be considered for the security. Here, we propose a zigzag approach to verify the phase-flip error of the survived bits after OPER or AOPP. Based on this, we can take all the finite-key effects efficiently in calculating the non-asymptotic key rate. Numerical simulation shows that our approach here produces the highest key rate over all distances among all existing methods, improving the key rate by more than 100% to 3000% in comparison with different prior art methods with typical experimental setting. These verify the advantages of the AOPP method with finite data size. Also, with our zigzag approach here, the non-asymptotic key rate of SNS-TF QKD can by far break the absolute bound of repeater-less key rate with whatever detection efficiency. We can even reach a non-asymptotic key rate more than 40 times of the practical bound and 13 times of the absolute bound with 1012 pulses.

Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, and practical devices are still not fully characterized for obtaining tight and realistic key rates. We present a simple method of computing secure key rates for any practical implementation of discrete-variable QKD (which can also apply to measurement-device-independent QKD), initially in the single-qubit lossless regime, and we rigorously prove its unconditional security against any possible attack. We hope our method becomes one of the standard tools used for analysing, benchmarking, and standardizing all practical realizations of QKD.

Genetic Algorithm (GA) may be used to analyses the security of Quantum Key Distribution (QKD) protocols. It evaluates on multiple QKD protocol such as, comparing it to known bounds and also discovering new results. It also shows how it can be used to analyze the security of complicated QKD protocols requiring the adversary to interact with the users. It may also be used to detect security flaws in protocols. This algorithm can be a useful tool in QKD research and design. The genetic algorithm can be used to analyses the security of the quantum cryptographic protocols. This paper handles the different types of attacks like photon loss and multi-photon attacks. Analysis can be done on these protocols namely BB84, B92, SARGO4, Semi-Quantum protocol, Mediated Semi-Quantum protocols. The attacks can be handled by using genetic algorithm is the main intention of this work.

<sec>Measurement-device-independent quantum key distribution (MDI-QKD) protocol can effectively resist all possible attacks targeting the measurement devices in a quantum key distribution (QKD) system, thus exhibiting high security. However, due to the protocol’s high sensitivity to channel attenuation, its key generation rate and transmission distance are significantly limited in practical applications.</sec><sec>To improve the performance of MDI-QKD, researchers have proposed quantum-memory (QM)-assisted MDI-QKD protocol, which has enhanced the protocol's performance to a certain extent. Nevertheless, under finite-size conditions where the total number of transmitted pulses is limited, accurately estimating the relevant statistical parameters is still a challenge. As a result, existing QM-assisted MDI-QKD schemes still encounters issues such as low key rates and limited secure transmission distances.</sec><sec>To solve these problems, this work proposes a novel improved finite-size QM-assisted MDI-QKD protocol. By utilizing quantum memories to temporarily store early-arriving pulses and release them synchronously, the protocol effectively reduces the influence caused by channel asymmetry. Additionally, the protocol introduces a four-intensity decoy-state method to improve the estimation accuracy of single-photon components. Meanwhile, to mitigate the influence of finite-length effects on QM schemes, the proposed protocol combines a collective constraint model and a double-scanning algorithm to jointly estimate scanning error counts and vacuum-related counts. This approach enhances the estimation accuracy of the single-photon detection rate and phase error rate under finite-size conditions, thereby significantly improving the secure key rate of the MDI-QKD system.</sec><sec>Simulation results show that under the same experimental conditions, compared with the existing QM-assisted three-intensity decoy-state MDI-QKD protocol and the four-intensity decoy-state MDI-QKD protocol based on Heralded Single-photon Source (HSPS), the proposed protocol extends the secure transmission distance by more than 30 km and 100 km, respectively. This proves that under the same parameter settings, the proposed scheme exhibits significant advantages in both key rate and secure transmission distance. Therefore, this research provides important theoretical references and valuable benchmarks for developing long-distance, high-security quantum communication networks.</sec>

The twin-field quantum key distribution (TF-QKD) protocol is designed to beat the rate-distance limit of quantum key distributions without employing quantum repeaters; meanwhile, it can offer the measurement-device-independent secure level. In this Letter, we propose to improve the performance of TF-QKD protocols by employing modified coherent states. Based on the Wang etal. sending-or-not scheme [Phys. Rev. A98, 062323 (2018)PLRAAN1050-294710.1103/PhysRevA.98.062323], we study the key rate with the modified coherent states in finite data size and do comparisons with the one using weak coherent states. Through numerical simulations, we demonstrate that modified coherent states can substantially increase the performance of QKD more than the latter.