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Physical Review Research

Security-rate trade-off in quantum key distribution: From individual links to large-scale networks

Stefano Pirandola, Cillian Harney, Gaetana Spedalieri

Published Jun 23, 2026• 1 citation
Publisher

Abstract

We explore the interplay between security and key rate of a quantum key distribution (QKD) protocol. This fundamental trade-off is investigated both at the link layer, i.e., for a QKD protocol implemented on a channel, and at the network layer, i.e., within the context of a multiuser multihop communication network. In the former scenario, we consider both discrete- and continuous-variable protocols in the composable finite-size framework, showing how their epsilon security restricts the key rate achievable on a single fiber link under various assumptions for the process of parameter estimation. In the latter scenario, we analyze the impact of composable security in the network setting, studying the interplay between end-to-end (ETE) epsilon security and ETE key rate for arbitrarily chosen remote end points. Starting from basic topologies to more complex ones, such as perturbed lattices, we analyze this trade-off under different types of routing strategies. In multipath routing, a greater number of paths can improve key rates, but this enhancement is accompanied by a reduction in the ETE security level. In the setting of single-path routing, we introduce a modified Dijkstra algorithm, which we call “lambda protocol,” able to optimize route construction depending on the joint ETE demand for security and rate. Our results are first derived for specific network instances (i.e., fixed topologies within a given network class) and subsequently extended to ensemble averages over entire network classes, where phase transitions are revealed with respect to node connectivity.

DOI
10.1103/7839-3xhy

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We explore the interplay between security and key rate of a quantum key distribution (QKD) protocol. This fundamental trade-off is investigated both at the link layer, i.e., for a QKD protocol implemented on a channel, and at the network layer, i.e., within the context of a multiuser multihop communication network. In the former scenario, we consider both discrete- and continuous-variable protocols in the composable finite-size framework, showing how their epsilon security restricts the key rate achievable on a single fiber link under various assumptions for the process of parameter estimation. In the latter scenario, we analyze the impact of composable security in the network setting, studying the interplay between end-to-end (ETE) epsilon security and ETE key rate for arbitrarily chosen remote end points. Starting from basic topologies to more complex ones, such as perturbed lattices, we analyze this trade-off under different types of routing strategies. In multipath routing, a greater number of paths can improve key rates, but this enhancement is accompanied by a reduction in the ETE security level. In the setting of single-path routing, we introduce a modified Dijkstra algorithm, which we call “lambda protocol,” able to optimize route construction depending on the joint ETE demand for security and rate. Our results are first derived for specific network instances (i.e., fixed topologies within a given network class) and subsequently extended to ensemble averages over entire network classes, where phase transitions are revealed with respect to node connectivity.
The efficacy of a communication network hinges upon both its physical architecture and the protocols that are employed within it. In the context of quantum communications, there exists a fundamental rate-loss trade-off for point-to-point quantum channels such that the rate for distributing entanglement, secret keys, or quantum states decays exponentially with respect to transmission distance. Quantum networks are the solution to overcome point-to-point limitations, but they simultaneously invite a challenging open question: How should quantum networks be designed to effectively and efficiently guarantee high rates? Now that performance and physical topology are inexorably linked, this question is not easy, but the answer is essential for a future quantum internet to be successful. In this work, we offer crucial insight into this open question for complex optical-fiber quantum networks. Using realistic descriptions of quantum networks via random network models and practical end-to-end routing protocols, we reveal critical phenomena associated with large-scale quantum networks. Our work reveals the weaknesses of applying single-path routing protocols within quantum networks, observing an inability to achieve reliable rates over long distances. Adapting algorithms for multipath routing, we employ an efficient and practical multipath routing algorithm capable of boosting performance while minimizing costly quantum resources.
Establishing scalable, secure quantum networks requires advancing beyond conventional point-to-point quantum key distribution (QKD) protocols toward point-to-multipoint QKD protocols. Here, we generalize a well-established discrete-modulated continuous-variable (CV) QKD protocol from the point-to-point to the point-to-multipoint setting. We present a comprehensive security analysis across different scenarios and derive secret key rates for loss-only and noisy channels, both in the asymptotic and the composable finite-size regime. Experimentally, we validate the protocol in a passive optical network with 10 km access links, achieving a composable secure key rate of 2.185×10 −3 bits per symbol (0.273 Mbit/s) against independent and identically distributed collective attacks. Our results demonstrate that discrete-modulated CV-QKD can support access networks with multiple users while relying solely on cost-efficient, off-the-shelf telecommunication components, paving the way toward practical, scalable, and secure quantum networks.
Quantum Key Distribution (QKD) networks enable unconditionally secure key exchange using quantum mechanical principles. However, routing cryptographic keys across multi-hop quantum networks introduces challenges unique to quantum communication. This survey analyzes and classifies 26 routing strategies proposed between 2013 and 2024 for terrestrial, satellite, and hybrid QKD infrastructures. Dynamic, key-aware routing algorithms have been shown to reduce service rejection rates by 25-40% compared to static shortest-path methods by incorporating real-time key pool availability and link error rates. Multi-path strategies improve resilience against trusted-node compromise by distributing keys across disjoint routes, albeit with an increase in key consumption of 30-60%. SDN-based orchestration frameworks emerge as essential enablers of flexible, QoS-aware routing for hybrid networks integrating terrestrial fibers and intermittent satellite links. Critical research directions include reducing dependence on trusted nodes through quantum repeaters or post-quantum cryptography, developing standardized key management interfaces for interoperability, and adopting AI-driven predictive routing for adapting to fluctuating network states. This comprehensive synthesis of routing algorithms, performance trade-offs, and unresolved issues offers practical guidance for engineering secure, adaptable, and large-scale QKD networks capable of meeting real-world deployment demands.
The paper addresses the Quantum Networks (QN) performance with Quantum Key Distribution (QKD) protocols.The focus is on networks with multi-hop paths (multiple QKD links with intermediate nodes).QKD emerged as a promising technology to ensure unconditioned communications security by exploiting the Quantum Computing (QC) and quantum principles.While the Point-to-Point (P2P) QKD links are well understood for several QKD protocols, the challenges concern the development of QN with multiple intermediate nodes and links.The deployment of quantum-secure communication systems over very large distances requires multi-hop QN.This paper presents a simulation-based case study for multi-hop QKD networks, focusing on the performance evaluation and the Cyber Security implications.The framework could be used to evaluate end-to-end key generation rates, latency, and resilience under various network topologies and link conditions.This methodology will allow to properly investigate how the network-level security policies can be integrated with QKD protocols to detect and mitigate both passive and active attacks.One could find out the trade-offs between hop count, security margins, and throughput, providing insights into the design of robust and scalable quantumsecure communication infrastructures.This study will support the research about the integration of the QKD with the classical network management, conventional security mechanisms and advanced Cyber defense strategies.
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.
Quantum key distribution (QKD) networks offer scalable secure communication, while efficient integration with existing optical infrastructure requires careful consideration. This paper investigates enhancing the security of multipath QKD over multi-band systems by exploring the trade-offs between multi-band separation and multipath techniques. A novel, to our knowledge, framework, incorporating blocking ratio analysis for a single and multipath QKD, is proposed, comparing bitwise product and concatenated key generation methods. Our model considers propagation delays and key pool synchronization’s impact on the secret key rate (SKR). Our simulations using a U.S. long-haul network model demonstrate significant benefits of implementing QKD in alternative spectral bands. The results show substantial improvements in SKR at various span lengths in single-path scenarios. Additionally, increasing the number of quantum channels led to noticeable reductions in network blocking rates, enabling higher classical traffic loads throughout the network infrastructure. We introduce, to our knowledge, new KPIs: the blocking rate ( B CQ ) and a comprehensive security rate ( C ), assessing the final key’s overall secrecy. For multipath schemes, simulations reveal that concatenated multipath QKD, while exhibiting a superior blocking rate, showed 12% less compromised secrecy at 4000 km (32% to 20%), compared to less than 10% for bitwise product multipath QKD under the same conditions. These findings provide valuable insights into designing efficient and secure quantum-enhanced optical networks, highlighting the complex interplay between security and efficiency in multipath QKD architectures.