We examine how the structural characteristics of entangled quantum states impact the achievable rates in entanglement-based quantum key distribution (QKD). Focusing on the performance differences between entangled states produced by entanglement distillation protocols and Werner states, we show that the structured nature of distilled states can yield significantly higher secure key rates, even when their fidelity matches that of Werner states. This suggests that while converting arbitrary entangled states into Werner states (through twirling) simplifies the analysis of protocol performance, it also limits potential secret key rates. Our findings underscore the potential of entanglement distillation protocols to enhance QKD performance by additionally improving the structure of entangled states, thus, broadening their utility beyond simple fidelity enhancement.
We examine how the structural characteristics of entangled quantum states impact the achievable rates in entanglement-based quantum key distribution (QKD). Focusing on the performance differences between entangled states produced by entanglement distillation protocols and Werner states, we show that the structured nature of distilled states can yield significantly higher secure key rates, even when their fidelity matches that of Werner states. This suggests that while converting arbitrary entangled states into Werner states (through twirling) simplifies the analysis of protocol performance, it also limits potential secret key rates. Our findings underscore the potential of entanglement distillation protocols to enhance QKD performance by additionally improving the structure of entangled states, thus, broadening their utility beyond simple fidelity enhancement.
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.
The following paper presents a holistic approach to the processing of entangled links within entanglement based quantum key distribution protocols, whose security relies on the Bell inequality. We investigate the interactions, and the collective impact, of the whole processing chain on the final secure key rate. This includes the quantum mechanical preprocessing in the form of entanglement distillation, processing of the entangled states via measurements and the necessary classical postprocessing based on the measurement results. Our investigations are based on the principle idea of the Eckert 1991 protocol and utilize the secret key capacity introduced by Devetak and Winter in 2005. Our results include a proof on what measurement bases need to be chosen to achieve this capacity for the case of Werner states. It also presents a new processing strategy and compares it with the most common one that can be found within the literature. Furthermore, it answers the question on how much entanglement distillation is optimal. By doing so we propose a unified formalism, describing the whole processing chain, that can be used to make quantitative statements on the relation between the quality and quantity of entangled but noisy quantum states used for generating secure keys.
It is crucial to share maximally entangled pairs in quantum information processing. However, unwanted interactions with the environment can reduce the entanglement fidelity of the produced pairs. Entanglement distillation is a method to overcome this problem by creating higher-fidelity entangled pairs from a more significant number of lower-fidelity pairs. This study uses Werner states and imperfect gates to analyse the performance of BBPSSW, DEJMPS, 3-to-1, and EPL protocols for entanglement distillation. Specifically, this study focuses on how the increase in fidelity depends on the input pair and gate fidelities. The results are obtained through numerical simulation using the NetSquid simulator. After characterising the numerical errors, the study demonstrates that all four protocols increase the pair fidelity for a gate higher than 0.96. The study also reveals that the higher the success fidelity, the lower the probability, as predicted theoretically. Additionally, based on a list of requirements and hardware performance, we developed a simple recipe for selecting the most suitable protocol. The simulation results highlight the practical limitations of entanglement distillation protocols, indicating the need for further investigation. This includes the development of a theoretical model for the EPL protocol implemented with Werner states, incorporating noisy measurements in the simulated protocols and increasing the number of simulations for higher accuracy.
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) achieves information-theoretic security for a shared secret key, using distributed quantum states. To establish secret bits, two honest parties apply key distillation protocols to the resulting measurement outcomes. In this work, we establish a rigorous connection between the key rate achievable by applying two-way key distillation, such as advantage distillation, and quantum hypothesis testing, via an integral representation of the conditional entropy in terms of the error probabilities of binary state discrimination. This connection significantly improves bounds on key rates at finite blocklengths relative to existing fidelity-based bounds. Moreover, in an important special case, it closes the gap between the known sufficient and conjectured necessary conditions for key generation in the large-blocklength limit. More generally, it establishes a matching asymptotic necessary condition, leaving the corresponding finite-blocklength result open. More broadly, our work shows how results in quantum hypothesis testing can directly sharpen the security analysis of QKD.
We investigate quantum repeaters in the context of quantum key distribution. We optimize the secret key rate per memory per second with respect to different distillation protocols and distillation strategies. For this purpose, we also derive an analytical expression for the average number of entangled pairs created by the quantum repeater, including classical communication times for entanglement swapping and entanglement distillation. We investigate the impact of this classical communication time on the secret key rate. Finally, we study the effect of the detector efficiency on the secret key rate.