Alternative schemes for twin-field quantum key distribution with discrete-phase-randomized sources

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 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.

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.

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.

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) 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.

Relativistic quantum key distribution (QKD) protocol is a kind of modified BB84 QKD protocol based on the principles of not only quantum mechanics but also special relativity. Its advantage compared with BB84 protocol is that all of the qubits could be used for key generation, and Alice and Bob are able to select any measuring bases. We prove its unconditional security against coherent attack via the method based on CSS codes: begin with a modified EPR based protocol which can be proved unconditionally secure, then reduce the protocol to a CSS codes based protocol. Finally, the CSS codes based protocol is demonstrated equivalent to the relativistic QKD protocol, and we arrived at the conclusion of the unconditional security of the final key.

Twin-Field Quantum Key Distribution (QKD) is a QKD protocol that uses single-photon interference to perform QKD over long distances. QKD protocols that encode information using high-dimensional quantum states can benefit from increased key rates and higher noise resilience. We define the essence of Twin-Field QKD and explore its generalization to higher dimensions. Further, we show that, ultimately, the Twin-Field protocol cannot be generalized to higher dimensions in accordance with our definition.

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.

<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>

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.

We investigate limitations imposed by sequential attacks on the performance of differential-phase-shift quantum key distribution protocols that use pulsed coherent light. In particular, we analyze two sequential attacks based on unambiguous state discrimination and minimum error discrimination, respectively, of the signal states emitted by the source. Sequential attacks represent a special type of intercept-resend attacks and, therefore, they provide ultimate upper bounds on the maximal distance achievable by quantum key distribution schemes.

The security of quantum communication using a weak coherent source requires\nan accurate knowledge of the source's mean photon number. Finite calibration\nprecision or an active manipulation by an attacker may cause the actual emitted\nphoton number to deviate from the known value. We model effects of this\ndeviation on the security of three quantum communication protocols: the\nBennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol without\ndecoy states, Scarani-Acin-Ribordy-Gisin 2004 (SARG04) QKD protocol, and a\ncoin-tossing protocol. For QKD, we model both a strong attack using technology\npossible in principle, and a realistic attack bounded by today's technology. To\nmaintain the mean photon number in two-way systems, such as plug-and-play and\nrelativistic quantum cryptography schemes, bright pulse energy incoming from\nthe communication channel must be monitored. Implementation of a monitoring\ndetector has largely been ignored so far, except for ID Quantique's commercial\nQKD system Clavis2. We scrutinize this implementation for security problems,\nand show that designing a hack-proof pulse-energy-measuring detector is far\nfrom trivial. Indeed the first implementation has three serious flaws confirmed\nexperimentally, each of which may be exploited in a cleverly constructed\nTrojan-horse attack. We discuss requirements for a loophole-free implementation\nof the monitoring detector.\n

Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.

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.