A Quantum Key Distribution (QKD) network is an infrastructure capable of performing long-distance and high-rate secret key agreement with information-theoretic security. In this paper we study security properties of QKD networks based on trusted repeater nodes. Such networks can already be deployed, based on current technology. We present an example of a trusted repeater QKD network, developed within the SECOQC project.
The main focus is put on the study of secure key agreement over a trusted repeater QKD network, when some nodes are corrupted. We propose an original method, able to ensure the authenticity and privacy of the generated secret keys.
We perform a numerical study of the distribution of entanglement on a real-world fiber grid connecting the German cities of Bonn and Berlin. The connection is realized using a chain of processing-node quantum repeaters spanning roughly 900 kilometers. We investigate how minimal hardware requirements depend on the target application, as well as on the number of repeaters in the chain. We find that requirements for blind quantum computing are markedly different than those for quantum key distribution, with the required coherence time being around two and a half times larger for the former. Furth…
As quantum key distribution becomes increasingly practical, questions of how to effectively employ it in large-scale networks and over large distances becomes increasingly important. To that end, in this work, we model the performance of the E91 entanglement based QKD protocol when operating in a network consisting of both quantum repeaters and trusted nodes. We propose a number of routing protocols for this network and compare their performance under different usage scenarios. Through our modeling, we investigate optimal placement and number of trusted nodes versus repeaters depending on devi…
In this paper we estimate how introduction of additional connections between trusted nodes through one, two and so on (i.e. connection density) to a quantum network with serial connection of trusted nodes affects its security. We provide proper scaling of failure probability of authentication and quantum key distribution protocols to the level of the whole quantum network. Expressions of the failure probability dependent on the total number of connected nodes between users and connection density for given mean failure probability of each element are derived. The result provides explicit trade-…
In this paper, we consider quantum key distribution (QKD) in a quantum network with both quantum repeaters and a small number of trusted nodes. In contrast to current QKD networks with only trusted nodes and the true Quantum Internet with only quantum repeaters, such networks represent a middle ground, serving as near-future QKD networks. In this setting, QKD can be efficiently and practically deployed, while providing insights for the future true Quantum Internet. To significantly improve the key generation efficiency in such networks, we develop a new dynamic routing strategy that makes rout…
Quantum key distribution is a way to distribute secret keys to distant users with information theoretic security and key rates suitable for real-world applications. Its rate-distance figure, however, is limited by the natural loss of the communication channel and can never surpass a theoretical limit known as point-to-point secret key capacity. Recently, a new type of quantum key distribution with an intermediate relay was proposed to overcome this limit (M. Lucamarini, Z. L. Yuan, J. F. Dynes and A. J. Shields, Nature, 2018). However, a standard application of the decoy state method limited t…
A recently published patent (https://www.ipo.gov.uk/p-ipsum/Case/PublicationNumber/GB2590064) has claimed the development of a novel quantum key distribution protocol purporting to achieve long-range quantum security without trusted nodes and without use of quantum repeaters. Here we present a straightforward analysis of this claim, and reach the conclusion that it is largely unfounded.
In quantum networking, repeater hijacking menaces the security and utility of quantum applications. To deal with this problem, it is important to take a measure of the impact of quantum repeater hijacking. First, we quantify the workload of each quantum repeater with regards to each quantum communication. Based on this, we show the costs for repeater hijacking detection using distributed quantum state tomography and the amount of work loss and rerouting penalties caused by hijacking. This quantitive evaluation covers both purification-entanglement swapping and quantum error correction repeater…
Quantum communication is developed owing to the theoretically proven security of quantum mechanics, which may become the main technique in future information security. However, most studies and implementations are limited to two or several parties. Herein, we propose a fully connected quantum communication network without a trusted node for a large number of users. Using flexible wavelength demultiplex/multiplex and space multiplex technologies, 40 users are fully connected simultaneously without a trusted node by a broadband energy-time entangled photon pair source. This network architecture …
In this paper, using the full security framework for continuous variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones.
Quantum key distribution (QKD) allows two distant parties to share encryption keys with security based on physical laws. Experimentally, it has been implemented with optical means, achieving key rates of 1.26 Megabit/s over 50 kilometres (km) of standard optical fibre and 1.16 bit/hour over 404 km of ultralow-loss fibre in a measurement-device-independent configuration. Increasing the bit rate and range of QKD is a formidable, but important, challenge. A related target, currently considered unfeasible without quantum repeaters, is overcoming the fundamental rate-distance limit of point-to-poin…
Variations of phase-matching measurement-device-independent quantum key distribution (PM-MDI QKD) protocols have been investigated before, but it was recently discovered that this type of protocol (under the name of twin-field QKD) can beat the linear scaling of the repeaterless bound on secret key rate capacity. We propose a variation of PM-MDI QKD protocol, which reduces the sifting cost and uses non-phase-randomized coherent states as test states. We provide a security proof in the infinite key limit. Our proof is conceptually simple and gives tight key rates. We obtain an analytical key ra…
Quantum key distribution (QKD) is the most used protocol in the context of quantum cryptography for sharing a private encryption key between two parties. Covid-19 pandemic has raised the ever-increasing need for online communications a lot; this requires enhanced security protocols. QKD has the potential to meet a global scale network's security requirements. Despite considerable progress, all ground-based QKD approaches have distance limitations due to atmospheric or fiber attenuation. A global network scheme can use intersatellite links to establish a trusted node network with constellations…
Discrete-modulated continuous-variable quantum key distribution protocols are promising candidates for large-scale deployment due to the large technological overlap with deployed modern optical communication devices. The security of discrete modulation schemes has previously analyzed in the ideal detector scenario in the asymptotic limit. In this work, we calculate asymptotic key rates against collective attacks in the trusted detector noise scenario. Our results show that we can thus cut out most of the effect of detector noise and obtain asymptotic key rates similar to those had we access to…
A quantum network is expected to enhance distributed quantum computing and quantum communication over a long distance while providing unconditional security. As quantum entanglement is essential for a quantum network, major issues from various types of noise and decoherence prevent it from being realized, and research has been intensively active to obtain optimal configurations for a quantum network. In this work, we address the performance of a quantum network capable of quantum error correction and entanglement purification. Our results show that one should distribute Bell pairs as fast as p…
Progress in the development of techniques for the construction of multiuser quantum communications networks is reviewed in light of the plans for an EU quantum communications infrastructure (EU QCI). Quantum key distribution networks may be classified as trusted node; quantum repeater-entanglement-swapping based; point-to-multipoint based on passive beam splitters, active optical switchers or WDM; high dimensional-multipartite entanglement and flexible reconfigurable multipartite networks. Both satellite and terrestrial implementations are possible and ore both planned for EU QCI; their relati…
Quantum communication is rapidly gaining popularity due to its high security and technological maturity. However, most implementations are limited to just two communicating parties (users). Quantum communication networks aim to connect a multitude of users. Here we present a fully connected quantum communication network on a city wide scale without active switching or trusted nodes. We demonstrate simultaneous and secure connections between all 28 pairings of 8 users. Our novel network topology is easily scalable to many users, allows traffic management features and minimises the infrastructur…
Quantum statistics can be considered from the perspective of postquantum no-signaling theories in which either none or only a certain number of quantum systems are trusted. In these scenarios, the role of states is played by the so-called no-signaling boxes or no-signaling assemblages respectively. It has been shown so far that in the usual Bell non-locality scenario with a single measurement run, quantum statistics can never reproduce an extremal non-local point within the set of no-signaling boxes. We provide here a general no-go rule showing that the latter stays true even if arbitrary sequ…
Long-distance quantum key distribution (QKD) has long time seriously relied on trusted relay or quantum repeater, which either has security threat or is far from practical implementation. Recently, a solution called twin-field (TF) QKD and its variants have been proposed to overcome this challenge. However, most security proofs are complicated, a majority of which could only ensure security against collective attacks. Until now, the full and simple security proof can only be provided with asymptotic resource assumption. Here, we provide a composable finite-key analysis for coherent-state-based…
Harnessing quantum processes is an efficient method to generate truly indeterministic random numbers, which are of fundamental importance for cryptographic protocols, security applications or Monte-Carlo simulations. Recently, quantum random number generators based on continuous variables have gathered a lot of attention due to the potentially high bit rates they can deliver. Especially quadrature measurements on shot-noise limited states have been studied in detail as they do not offer any side information to potential adversaries under ideal experimental conditions. However, they may be subj…
We show that partially trusting the phase noise associated with estimation uncertainty in a LLO CVQKD system allows one to exchange higher secure key rates than in the case of untrusted phase noise. However, this opens a security loophole through the manipulation of the reference pulse amplitude. We label this as "reference pulse attack" which is applicable to all LLO-CVQKD systems if the phase noise is trusted. We show that, at the optimal reference pulse intensity level, Eve achieves unity attack efficiency at 23.8km and 32.0km while using lossless and 0.14dB/km loss channels, respectively, …
We propose a quantum k-means algorithm based on quantum cloud computing that effectively solves the problem that the client can not afford to execute the same quantum subroutine repeatedly in the face of large training samples. In the quantum k-means algorithm, the core subroutine is the Quantum minimization algorithm (GroverOptim), the client needs to repeat several Grover searches to find the minimum value in each iteration to find a new clustering center, so we use quantum homomorphic encryption scheme (QHE) to encrypt the data and upload it to the cloud for computing. After calculation, th…
Distribution and distillation of entanglement over quantum networks is a basic task for Quantum Internet applications. A fundamental question is then to determine the ultimate performance of entanglement distribution over a given network. Although this question has been extensively explored for bipartite entanglement-distribution scenarios, less is known about multipartite entanglement distribution. Here we establish the fundamental limit of distributing multipartite entanglement, in the form of GHZ states, over a quantum network. In particular, we determine the multipartite entanglement distr…
Quantum networks open the way to an unprecedented level of communication security. However, due to physical limitations on the distances of quantum links, current implementations of quantum networks are unavoidably equipped with trusted nodes. As a consequence, the quantum key distribution can be performed only on the links. Due to this, some new authentication and key exchange schemes must be considered to fully benefit from the unconditional security of links. One such approach uses Multiple Non-Overlapping Paths (MNOPs) for key exchange to mitigate the risk of an attack on a trusted node. T…
Security of practical continuous-variable quantum key distribution is addressed and a security analysis framework, which does not rely on phase-space symmetries of signal states and correlations, is developed. In a general purification-based approach, following optimality of Gaussian collective attacks, it is suggested to find an equivalent generally mixed two-mode state shared between the trusted parties and then purifying it using Bloch-Messiah decomposition. This allows to assess security of the schemes with arbitrary parameters, which can be typically expected in experiments. It also allow…
Distributed Denial-of-Service (DDoS) attacks can occur in quantum networks, which can pose a significant threat to its key distribution protocols. We introduce a quantum analogue of a classical entropic DDoS detection system, and apply it in the context of detecting an attack on a quantum network. In particular, we examine DDoS attacks on a quantum repeater and harness the associated entanglement entropy for the detection system. Our method contributes to the applicability of quantum information from the domain of data security to the area of network security.
We introduce a ternary quantum key distribution (QKD) protocol and asymptotic security proof based on three coherent states and homodyne detection. Previous work had considered the binary case of two coherent states and here we nontrivially extend this to three. Our motivation is to leverage the practical benefits of both discrete and continuous (Gaussian) encoding schemes creating a best-of-both-worlds approach; namely, the postprocessing of discrete encodings and the hardware benefits of continuous ones. We present a thorough and detailed security proof in the limit of infinite signal states…
