Quantum key distribution (QKD) enables two remote users to share a string of key bits with information-theoretical security. Parameter optimization is a crucial step in achieving optimal performance in practical QKD systems. In general, such optimization is implemented using a local search algorithm (LSA). However, LSAs inevitably fail to find out the optimal values when the searched key rate function is nonconvex or has a discontinuity of first-order derivatives and a narrow parameter search space. This paper proposes a genetic algorithm-based method to overcome the limitations of LSAs for QKD parameter optimization. We tested the proposed method with various types of common QKD protocols and found that it has very high parameter optimization performance for QKD with a time consumption comparable to that using a standard LSA. We expect our method to be a valuable optimization tool for quantum information processing tasks.
Quantum key distribution (QKD) enables two remote users to share a string of key bits with information-theoretical security. Parameter optimization is a crucial step in achieving optimal performance in practical QKD systems. In general, such optimization is implemented using a local search algorithm (LSA). However, LSAs inevitably fail to find out the optimal values when the searched key rate function is nonconvex or has a discontinuity of first-order derivatives and a narrow parameter search space. This paper proposes a genetic algorithm-based method to overcome the limitations of LSAs for QKD parameter optimization. We tested the proposed method with various types of common QKD protocols and found that it has very high parameter optimization performance for QKD with a time consumption comparable to that using a standard LSA. We expect our method to be a valuable optimization tool for quantum information processing tasks.
Abstract 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 thekey-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.
Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual performance of former demonstrations. Here, we present analytical and numerical decoy-state methods with one, two, and three decoy states. We provide a clear comparison among these methods and find that two decoy states already enable a near-optimal estimation and more decoy states cannot improve the key rate much in either asymptotic or finite-data settings. Furthermore, we perform a full optimization of system parameters and show that full optimization can significantly improve the key rate in the finite-data setting. By simulating a real experiment, we find that full optimization can increase the key rate by more than one order of magnitude compared to nonoptimization. A local search method to optimize efficiently the system parameters is proposed. This method can be four orders of magnitude faster than a trivial exhaustive search to achieve a similar optimal key rate. We expect that this local search method could be valuable for general fields in physics.
For a practical quantum key distribution (QKD) system, parameter optimization, the choice of intensities and the probabilities of sending them, is a crucial step in gaining optimal performance, especially when one realistically considers a finite communication time. With the increasing interest in the field to implement QKD over free space on moving platforms, such as drones, handheld systems, and even satellites, one needs to perform parameter optimization with low latency and with very limited computing power. Moreover, with the advent of the internet of things, a highly attractive direction of QKD could be a quantum network with multiple devices and numerous connections, which provides a huge computational challenge for the controller that optimizes parameters for a large-scale network. Traditionally, such an optimization relies on brute-force search or local search algorithms, which are computationally intensive, and will be slow on low-power platforms (which increases latency in the system) or infeasible for even moderately large networks. In this work we present a method that uses a neural network to directly predict the optimal parameters for QKD systems. We test our machine learning algorithm on hardware devices including a Raspberry Pi 3 single-board computer (similar devices are commonly used on drones) and a mobile phone, both of which have a power consumption of less than 5 W, and we find a speedup of up to two to four orders of magnitude when compared to standard local search algorithms. The predicted parameters are highly accurate and can preserve, e.g., over 95%--99% of the optimal secure key rate for a given protocol. Moreover, our approach is highly general and can be applied effectively to various kinds of common QKD protocols.
In quantum-classical coexistence systems, classical noise and system loss can significantly affect the performance of quantum key distribution (QKD), while the fixed-parameter QKD (FPQ) cannot adapt to varying conditions. In this paper, we propose a local search algorithm (LSA) for QKD to optimize the parameters in wavelength division multiplexing (WDM) and space division multiplexing (SDM) systems. Simulation results show that LSA can achieve 99.9% performance of the exhaustive search algorithm, while significantly reducing computational complexity. Moreover, LSA improves QKD performance by 31.9% over standard single mode fiber and 24.5% over multicore fiber in quantum-classical coexistence systems.
We investigate the optimization of epsilon-security parameters in quantum key distribution (QKD), aiming to improve the achievable secure key rate under a fixed overall composable security level. For this purpose, we employ a continuous genetic algorithm (CGA) to optimize the epsilon-security components of two representative protocols: the homodyne protocol from the continuous-variable (CV) family and the BB84 protocol from the discrete-variable (DV) family. We detail the CGA configuration, summarize the derivation of the composable key rate, and emphasize the role of the epsilon-parameters in both protocols. We then compare key rates obtained with optimized epsilon-values against those derived from standard and randomized choices. Our results demonstrate substantial key rate improvements at high security levels, where the key rate typically vanishes, and uncover positive-rate regimes that are inaccessible without optimization.
Abstract As the number of users in quantum key distribution (QKD) networks continues to grow, parameter selection (e.g., probability of X-bases, signal state strength, and decoy state levels) has become increasingly complex. Traditional methods such as local search algorithms (LSA) are commonly employed for parameter optimization but suffer from significant computational overhead, slow execution on low-power platforms, and resultant system delays. These limitations hinder the scalability and real-time requirements of large-scale QKD networks. To address these challenges, this paper proposes an innovative approach that combines Bayesian optimization with XGBoost model to optimize QKD system parameters. The proposed model is evaluated against random forest (RF) and back-propagation neural network (BPNN) models based on three critical metrics: prediction accuracy, model fitting, and training efficiency. Simulation results demonstrate that the proposed model significantly outperforms both RF and BPNN in terms of accuracy and computational efficiency. Notably, while achieving predictive performance comparable to LSA, the proposed method reduces computation time by three orders of magnitude. This research introduces a novel and efficient framework for QKD parameter optimization, providing new insights and directions for enhancing the performance, scalability, and real-time adaptability of QKD systems.