Quantum Key Distribution (QKD) represents a revolutionary approach in the field of cryptography, offering the potential for unconditional security by leveraging the principles of quantum mechanics. This paper addresses the crucial issue of calculating secure key rates in entanglement based QKD systems. We present a method of key rate calculations that is independent of an eavesdropper's quantum system, relying solely on the quantum states shared between two communicating parties under the assumption of a worst-case attack. We undertake a comparison of asymptotic key rates with those observed in the finite regime, in which only a limited number of quantum states are exchanged. Furthermore, we investigate the influence of entanglement distillation on the achievable key rates. By identifying the numerically optimal number of entanglement distillation iterations based on the initial fidelity and the number of exchanged quantum states, we demonstrate how to achieve a balance between the quantity and quality of entangled states, thereby maximizing the secure key rate. Our results show that there is a unique optimum within a defined search range. Moreover, we determine the minimum number of exchanged quantum states necessary to attain a positive key rate and to obtain a desired number of secure key bits, which are both contingent upon the quality of the communication channel. It is anticipated that the insights gained from this work will prove instrumental in the development of optimal routing strategies in quantum communication networks.
Quantum Key Distribution (QKD) represents a revolutionary approach in the field of cryptography, offering the potential for unconditional security by leveraging the principles of quantum mechanics. This paper addresses the crucial issue of calculating secure key rates in entanglement based QKD systems. We present a method of key rate calculations that is independent of an eavesdropper's quantum system, relying solely on the quantum states shared between two communicating parties under the assumption of a worst-case attack. We undertake a comparison of asymptotic key rates with those observed in the finite regime, in which only a limited number of quantum states are exchanged. Furthermore, we investigate the influence of entanglement distillation on the achievable key rates. By identifying the numerically optimal number of entanglement distillation iterations based on the initial fidelity and the number of exchanged quantum states, we demonstrate how to achieve a balance between the quantity and quality of entangled states, thereby maximizing the secure key rate. Our results show that there is a unique optimum within a defined search range. Moreover, we determine the minimum number of exchanged quantum states necessary to attain a positive key rate and to obtain a desired number of secure key bits, which are both contingent upon the quality of the communication channel. It is anticipated that the insights gained from this work will prove instrumental in the development of optimal routing strategies in quantum communication networks.
Abstract Quantum key distribution (QKD) allows for secure communications safe against attacks by quantum computers. QKD protocols are performed by sending a sizeable, but finite, number of quantum signals between the distant parties involved. Many QKD experiments, however, predict their achievable key rates using asymptotic formulas, which assume the transmission of an infinite number of signals, partly because QKD proofs with finite transmissions (and finite-key lengths) can be difficult. Here we develop a robust numerical approach for calculating the key rates for QKD protocols in the finite-key regime in terms of two semi-definite programs (SDPs). The first uses the relation between conditional smooth min-entropy and quantum relative entropy through the quantum asymptotic equipartition property, and the second uses the relation between the smooth min-entropy and quantum fidelity. The numerical programs are formulated under the assumption of collective attacks from the eavesdropper and can be promoted to withstand coherent attacks using the postselection technique. We then solve these SDPs using convex optimization solvers and obtain numerical calculations of finite-key rates for several protocols difficult to analyze analytically, such as BB84 with unequal detector efficiencies, B92, and twin-field QKD. Our numerical approach democratizes the composable security proofs for QKD protocols where the derived keys can be used as an input to another cryptosystem.
Realizing secure communication between distant parties is one of the main goals of quantum technology. Although quantum key distribution (QKD) promises information-theoretic security for sharing a secret key, the key rate heavily depends on the level of noise in the quantum channel. To overcome the noise, both quantum and classical techniques exist, i.e., entanglement distillation and classical advantage distillation. So far, these techniques have only been used separately from each other. Herein, we present a two-stage distillation scheme concatenating entanglement distillation with classical advantage distillation. For the advantage distillation, we utilize a fixed protocol, specifically, the repetition code; in the case of entanglement distillation, we employ an enumeration algorithm to find an optimal protocol. We test our scheme for noisy entangled states and demonstrate its quantitative advantage: Our two-stage distillation scheme achieves finite key rates even in a high-noise regime where entanglement distillation or advantage distillation alone cannot afford key sharing. We also calculate the security bounds for relevant QKD protocols with our key-distillation scheme and show that they exceed the previous security bounds on the critical quantum bit error rates with only advantage distillation. Since the advantage distillation part does not introduce further requirements for quantum resources other than those required for entanglement distillation, the proposed scheme is well suited for quantum key distribution tasks with entanglement distribution networks.
Quantum key distribution (QKD) allows unconditionally secure communication based on the laws of quantum mechanics rather than assumptions about computational hardness. Optimizing the operation parameters of a given QKD implementation is indispensable in order to achieve high secure key rates. So far, there exists no model that accurately describes entanglement-based QKD with continuous-wave pump lasers. We analyze the underlying mechanisms for QKD with temporally uniform pair-creation probabilities and develop a simple but accurate model to calculate optimal tradeoffs for maximal secure key rates. In particular, we find an optimization strategy of the source brightness for given losses and detection-time resolution. All experimental parameters utilized by the model can be inferred directly in standard QKD implementations, and no additional assessment of device performance is required. Comparison with experimental data shows the validity of our model. Our results yield a tool to determine optimal operation parameters for already existing QKD systems, to plan a full QKD implementation from scratch, and to determine fundamental key rate and distance limits of given connections.
The promise of unconditional security in the Quantum Key Distribution (QKD) depends on the availability of an authenticated classical channel. However, practical implementations often overlook this requirement or rely on computational assumptions that compromise long-term security. To overcome these challenges, this paper presents Entanglement-Based Authenticated Quantum Key Distribution (EAQKD), a novel protocol that addresses critical security and practical limitations in quantum cryptographic key exchange. Our approach integrates quantum entanglement distribution with information-theoretic authentication. We evaluate EAQKD's performance through a comprehensive discrete-event simulation framework modeled on realistic channel characteristics and experimental device parameters. Our modeling incorporates parameters from practical quantum optics setups, including SPDC entanglement sources, superconducting nanowire detectors, and fiber channel imperfections. Our results show quantum bit error rates consistently below the 11% security threshold (ranging from 1.86% at 10 km to 9.27% at 200 km), with secure key rates achieving 1.12×105 bits/s at short distances and maintaining practical rates of 9.8 bits/s at 200 km. When integrated with quantum repeater architectures, our analysis projects that EAQKD can extend secure communication beyond 500 km while providing information-theoretic security guarantees. Comparative analysis against the BB84, E91, and Twin-Field QKD protocols demonstrates EAQKD's superior balance of security, practical performance, and implementation robustness. This work advances quantum cryptography by providing a rigorously analyzed engineering reference for secure key distribution in future quantum communication networks.
Quantum key distribution (QKD) enables secure information exchange with untrusted quantum links between remote communication parties. A central task in the studies of QKD protocols is security analysis, which aims at deriving the length of the final key such that it is secure regardless of the eavesdropper's computational power. In literature, the security analysis has been done both analytically and numerically. Compared to analytical methods which tend to require techniques specific to each QKD protocol, numerical ones are more general since they can be directly applied to many QKD protocols with little adaptation. However, current numerical methods are carried out based on some assumptions such as working in the asymptotic limit and collective attacks from eavesdroppers. In this work, we remove these assumptions and develop a numerical finite-size security analysis against general attacks for a large class of QKD protocols. We also give an example of applying the method to the recent phase-matching QKD protocol with a simplified protocol design. Our result shows that the finite-size key rate can surpass the linear key-rate bound with a practical QKD system operated for only several hours.
As digital communication continues to expand across critical infrastructures, ensuring data security has become more challenging in the face of advancing computational capabilities, especially with the anticipated rise of quantum computers. Quantum Key Distribution (QKD) presents a revolutionary approach to secure communications by leveraging the fundamental principles of quantum mechanics, such as superposition and entanglement, to enable the secure exchange of cryptographic keys. Unlike classical encryption methods that rely on computational complexity, QKD ensures unconditional security, as any attempt to intercept the key disturbs the quantum state, revealing the presence of eavesdroppers. This paper explores the current developments in QKD protocols, including BB84 and E91, as well as practical challenges in implementation, such as distance limitations and hardware requirements. Furthermore, it discusses recent advancements in satellite-based QKD, integrated photonics, and quantum networks, highlighting their potential to reshape the landscape of secure global communication. The integration of QKD into future communication infrastructure is positioned to be a cornerstone of post-quantum cryptography, making it a vital technology in the era of quantum computing.