Quantum Key Distribution Links Research Articles

Linking QKD Testbeds across Europe.

Quantum-key-distribution (QKD) networks are gaining importance and it has become necessary to analyze the most appropriate methods for their long-distance interconnection. In this paper, four different methods of interconnecting remote QKD networks are proposed. The methods are used to link three different QKD testbeds in Europe, located in Berlin, Madrid, and Poznan. Although long-distance QKD links are only emulated, the methods used can serve as a blueprint for the secure interconnection of distant QKD networks in the future. Specifically, the presented approaches combine, in a transparent way, different fiber and satellite physical media, as well as common standards of key delivery interfaces. The testbed interconnections are designed to increase the security by utilizing multipath techniques and multiple hybridizations of QKD and post-quantum cryptography (PQC) algorithms.

Multiplexing Quantum and Classical Channels of a Quantum Key Distribution (QKD) System by Using the Attenuation Method

The primary goal in this paper is to verify the possibility of combining a quantum channel into a single optical fiber with other classical channels by using the so-called attenuation method. Since the quantum channel is very weak in terms of power, combining it into a single fiber with much more powerful classical channels is challenging. Thus, sufficiently high-quality filtering is important to avoid possible crosstalk. A second and more difficult problem to address is the interference caused by Raman noise, which increases with the fiber length and is also dependent on the input power of the classical channel. Thus, in this paper the focus is on the possibility of suppressing the Raman noise effect, both in advance by means of wavelength positioning and by means of installed optical components. Such phenomena must be considered in the route design, as the quantum channel must be placed at a suitable wavelength with respect to the classical channels. The influence of other nonlinear phenomena has been neglected. In this paper, a practical experiment aimed at building a fully functional multiplexed quantum key distribution link is also described.

Experimental Demonstration of Fully Passive Quantum Key Distribution.

The passive approach to quantum key distribution (QKD) consists of removing all active modulation from the users' devices, a highly desirable countermeasure to get rid of modulator side channels. Nevertheless, active modulation has not been completely removed in QKD systems so far, due to both theoretical and practical limitations. In this Letter, we present a fully passive time-bin encoding QKD system and report on the successful implementation of a modulator-free QKD link. According to the latest theoretical analysis, our prototype is capable of delivering competitive secret key rates in the finite key regime.

Statistical verifications and deep-learning predictions for satellite-to-ground quantum atmospheric channels

Laser communications from small satellite platforms empowers the establishment of quantum key distribution (QKD), relying on quantum superposition states of single photons to realize unconditional security between distant parties at a global scale. Although recent breakthrough experiments have demonstrated the feasibility of satellite-to-ground QKD links, the underlying statistical characteristics of quantum atmospheric channels have not been well-understood and experimentally verified in the literature. In this paper, we highlight that classical atmospheric statistical models can be applied for describing random fluctuations of the quantum channels. To verify this fact, we report a statistical verification study of quantum atmospheric channels from the world’s first low-Earth orbit (LEO) 50-kg-class microsatellite-to-ground quantum-limited communication experiment. The verified statistical model is then applied to numerically investigate the quantum bit-error rate (QBER) and secret-key length (SKL) of a decoy-state efficient Bennett-Brassard 1984 (BB84) QKD protocol with optimized parameters considering finite-key effects, implemented over a LEO 6-unit (6U)-CubeSat-to-ground link. Important insights of the physical channel effects including pointing errors and atmospheric turbulence on the QBER and SKL are then revealed. Finally, we present a study using a deep-learning-based long short-term memory (LSTM) recurrent neural network (RNN) for predicting photon-count fluctuations over quantum atmospheric channels.

40-user fully connected entanglement-based quantum key distribution network without trusted node

Quantum key distribution (QKD) would play an important role in future information technologies due to its theoretically proven security based on the laws of quantum mechanics. How to realize QKDs among multiple users in an effective and simple way is crucial for its real applications in communication networks. In this work, we propose and demonstrate a fully connected QKD network without trusted node for a large number of users. Using flexible wavelength division multiplexing/demultiplexing and space division multiplexing, entanglement resources generated by a broadband energy-time entangled quantum light source are distributed to 40 users. Any two users share a part of entanglement resources, by which QKD is established between them. As a result, it realizes a fully connected network with 40 users and 780 QKD links. The performance of this network architecture is also discussed theoretically, showing its potential on developing quantum communication networks with large user numbers owing to its simplicity, scalability, and high efficiency.

LEO Satellites Constellation-to-Ground QKD Links: Greek Quantum Communication Infrastructure Paradigm

Quantum key distribution (QKD) has gained a lot of attention over the past few years, but the implementation of quantum security applications is still challenging to accomplish with the current technology. Towards a global-scale quantum-secured network, satellite communications seem to be a promising candidate to successfully support the quantum communication infrastructure (QCI) by delivering quantum keys to optical ground terminals. In this research, we examined the feasibility of satellite-to-ground QKD under daylight and nighttime conditions using the decoy-state BB84 QKD protocol. We evaluated its performance on a hypothetical constellation with 10 satellites in sun-synchronous Low Earth Orbit (LEO) that are assumed to communicate over a period of one year with three optical ground stations (OGSs) located in Greece. By taking into account the atmospheric effects of turbulence as well as the background solar radiance, we showed that positive normalized secure key rates (SKRs) up to 3.9×10−4 (bps/pulse) can be obtained, which implies that satellite-to-ground QKD can be feasible for various conditions, under realistic assumptions in an existing infrastructure.

Soft decoding of short/medium length codes using ordered statistics for quantum key distribution

Quantum key distribution (QKD) is a cryptographic communication protocol that utilizes quantum mechanical properties for provable absolute security against an eavesdropper. The communication is carried between two terminals using random photon polarization states represented through quantum states. Both these terminals are interconnected through disjoint quantum and classical channels. Information reconciliation using delay controlled joint decoding is performed at the receiving terminal. Its performance is characterized using data and error rates. Achieving low error rates is particularly challenging for schemes based on error correcting codes with short code lengths. This article addresses the decoding process using ordered statistics decoding for information reconciliation of both short and medium length Bose–Chaudhuri–Hocquenghem codes over a QKD link. The link’s quantum channel is modeled as a binary symmetric quantum depolarization channel, whereas the classical channel is configured with additive white Gaussian noise. Our results demonstrate the achievement of low bit error rates, and reduced decoding complexity when compared to other capacity achieving codes of similar length and configuration.

Evaluation of eavesdropping error-rates in higher-dimensional QKD system implemented using dynamic spatial modes

Secure exchange of cryptographic keys is extremely important for any communication system where security and privacy of data is desirable. Although classical cryptographic algorithms provide computationally secure methods for secret key exchange, quantum key distribution (QKD) provides an extraordinary means to this end by guaranteeing unconditional security. Any malicious interception of communication by a man-in-the-middle on a QKD link immediately alerts sender and receiver by introducing an unavoidable error-rate. Higher-dimensional QKD protocols such as KMB09 exhibit higher eavesdropping error-rates with improved intrusion detection but their practical implementation is still awaited. In this paper, we present the design and implementation of KMB09 protocol using Laguerre–Gaussian orbital angular momentum to demonstrate and highlight the advantages of using dynamic spatial modes in QKD system. A complete error-rate analysis of KMB09 protocol implementation is presented with two different types of eavesdropping error-rates. Furthermore, we also demonstrate the decoy state method to show the robustness of the protocol against photon-number-splitting attack.

Twin-Field Quantum Key Distribution with Fully Discrete Phase Randomization

Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them have already been implemented experimentally. Most of them assume that the users can emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close this loophole, we propose and prove the security of a TF-QKD variant that relies exclusively on discrete phase randomisation. Remarkably, our results show that it can also provide higher secret-key rates than counterpart protocols that rely on continuous phase randomisation.

An integrated space-to-ground quantum communication network over 4,600 kilometres.

Quantum key distribution (QKD)1,2 has the potential to enable secure communication and information transfer3. In the laboratory, the feasibility of point-to-point QKD is evident from the early proof-of-concept demonstration in the laboratory over 32 centimetres4; this distance was later extended to the 100-kilometre scale5,6 with decoy-state QKD and more recently to the 500-kilometre scale7-10 with measurement-device-independent QKD. Several small-scale QKD networks have also been tested outside the laboratory11-14. However, a global QKD network requires a practically (not just theoretically) secure and reliable QKD network that can be used by a large number of users distributed over a wide area15. Quantum repeaters16,17 could in principle provide a viable option for such a global network, but they cannot be deployed using current technology18. Here we demonstrate an integrated space-to-ground quantum communication network that combines a large-scale fibre network of more than 700 fibre QKD links and two high-speed satellite-to-ground free-space QKD links. Using a trusted relay structure, the fibre network on the ground covers more than 2,000 kilometres, provides practical security against the imperfections of realistic devices, and maintains long-term reliability and stability. The satellite-to-ground QKD achieves an average secret-key rate of 47.8 kilobits per second for a typical satellite pass-more than 40 times higher than achieved previously. Moreover, its channel loss is comparable to that between a geostationary satellite and the ground, making the construction of more versatile and ultralong quantum links via geosynchronous satellites feasible. Finally, by integrating the fibre and free-space QKD links, the QKD network is extended to a remote node more than 2,600 kilometres away, enabling any user in the network to communicate with any other, up to a total distance of 4,600 kilometres.

A Novel Approach to Quality-of-Service Provisioning in Trusted Relay Quantum Key Distribution Networks

In recent years, noticeable progress has been made in the development of quantum equipment, reflected through the number of successful demonstrations of Quantum Key Distribution (QKD) technology. Although they showcase the great achievements of QKD, many practical difficulties still need to be resolved. Inspired by the significant similarity between mobile ad-hoc networks and QKD technology, we propose a novel quality of service (QoS) model including new metrics for determining the states of public and quantum channels as well as a comprehensive metric of the QKD link. We also propose a novel routing protocol to achieve high-level scalability and minimize consumption of cryptographic keys. Given the limited mobility of nodes in QKD networks, our routing protocol uses the geographical distance and calculated link states to determine the optimal route. It also benefits from a caching mechanism and detection of returning loops to provide effective forwarding while minimizing key consumption and achieving the desired utilization of network links. Simulation results are presented to demonstrate the validity and accuracy of the proposed solutions.

Programmable Quantum Networked Microgrids

Quantum key distribution (QKD) provides a potent solution to securely distribute keys for two parties. However, QKD itself is vulnerable to denial of service (DoS) attacks. A flexible and resilient QKD-enabled networked microgrids (NMs) architecture is needed but does not yet exist. In this article, we present a programmable quantum NMs (PQNMs) architecture. It is a novel framework that integrates both QKD and software-defined networking (SDN) techniques capable of enabling scalable, programmable, quantum-engineered, and ultra-resilient NMs. Equipped with a software-defined adaptive post-processing approach, a two-level key pool sharing strategy and an SDN-enabled event-triggered communication scheme, these PQNMs mitigate the impact of DoS attacks through programmable post-processing and secure key sharing among QKD links, a capability unattainable using existing technologies. Through comprehensive evaluations, we validate the benefits of PQNMs and demonstrate the efficacy of the presented strategies under various circumstances. Extensive results provide insightful resources for building QKD-enabled NMs in practice.

Telecommunication Compatibility Evaluation for Co-existing Quantum Key Distribution in Homogenous Multicore Fiber

Quantum key distribution (QKD) is regarded as an alternative to traditional cryptography methods for securing data communication by quantum mechanics rather than computational complexity. Towards the massive deployment of QKD, embedding it with the telecommunication system is crucially important. Homogenous optical multi-core fibers (MCFs) compatible with spatial division multiplexing (SDM) are essential components for the next-generation optical communication infrastructure, which provides a big potential for co-existence of optical telecommunication systems and QKD. However, the QKD channel is extremely vulnerable due to the fact that the quantum states can be annihilated by noise during signal propagation. Thus, investigation of telecom compatibility for QKD co-existing with high-speed classical communication in SDM transmission media is needed. In this paper, we present analytical models of the noise sources in QKD links over heterogeneous MCFs. Spontaneous Raman scattering and inter-core crosstalk are experimentally characterized over spans of MCFs with different refractive index profiles, emulating shared telecom traffic conditions. Lower bounds for the secret key rates and quantum bit error rate (QBER) due to different core/wavelength allocation are obtained to validate intra- and inter-core co-existence of QKD and classical telecommunication.

Simple security proof of twin-field type quantum key distribution protocol

Twin-field (TF) quantum key distribution (QKD) was conjectured to beat the private capacity of a point-to-point QKD link by using single-photon interference in a central measuring station. This remarkable conjecture has recently triggered an intense research activity to prove its security. Here, we introduce a TF-type QKD protocol which is conceptually simpler than the original proposal. It relies on the pre-selection of a global phase, instead of the post-selection of a global phase, which significantly simplifies its security analysis and is arguably less demanding experimentally. We demonstrate that the secure key rate of our protocol has a square-root improvement over the point-to-point private capacity, as conjectured by the original TF QKD.

Cost-Efficient Quantum Key Distribution (QKD) Over WDM Networks

Quantum key distribution (QKD) uses the laws of quantum mechanics to distribute secret keys with information-theoretic security. To realize QKD for secure communications among multiple distant users, fiber-based QKD networks can be deployed with today's available technologies. Incorporating QKD into existing wavelength-division multiplexing (WDM) network infrastructure provides a practical way to reduce the difficulty and cost of QKD networking. Nonetheless, the costs of QKD nodes and QKD links are still considered as the major barriers to long-distance QKD network deployment in practice. In this work, we study how to minimize the cost of deploying QKD-over-WDM backbone networks. We introduce a general architecture of QKD-over-WDM backbone networks. A novel cost-oriented model is defined to elaborate the cost-minimized problem, in which various QKD network components including QKD transceivers, QKD auxiliary equipment for QKD backbone nodes and trusted repeater nodes (TRNs), and QKD links are considered. The physical-layer parameters such as secret-key rate, physical distance, and the layout of TRNs are also incorporated in our defined model. We develop an integer linear programming (ILP) model and a novel cost-efficient QKD networking (CEQN) heuristic algorithm to address the cost-minimized problem. The extensive simulations indicate that our proposed approaches are effective in reducing the cost of deploying QKD-over-WDM backbone networks, where the designed CEQN algorithm is efficient to demonstrate similar to the ILP model. Finally, some open issues in future work are discussed, given that this work only presents an early highlevel analysis as opposed to a definitive detailed model.

Free space quantum key distribution using modulating retro-reflectors.

Quantum key distribution (QKD) can be used to produce a cryptographic key whose security is guaranteed by quantum mechanics. The range of fiber-based QKD links is limited, by loss, to a few hundred kilometers, and cannot be used between mobile platforms. Free space QKD can, in principle, overcome these limitations. In practice, very narrow beam divergences must be used, requiring highly accurate pointing of the transmitting terminal to the receiver. This makes deployment very difficult. Here we describe the experimental implementation of a new type of free space QKD link, using modulating retro-reflectors (MRR). The MRR-QKD link eases the pointing requirements by more than three orders of magnitude, from microradians to degrees, while maintaining the narrow beam divergence necessary for long-range communication links. The system uses new, high extinction surface-normal multiple quantum well modulators with a modulation rate of 100 MHz. A laboratory-based BB84 QKD link using multiple quantum well MRRs is demonstrated, link budgets for possible applications are discussed, and security issues are considered.

Analysis of the Public Channel of Quantum Key Distribution Link

Quantum key distribution (QKD) relies on the laws of physics to establish a symmetric binary key between remote parties. A QKD link involves the realization of a quantum channel for the transmission of quantum key material encoded in certain photon properties, as well as a public channel for verification of the exchanged key material. This paper deals with the mutual dependence of these channels and analyzes the impact of performance of both channels on the overall key material establishment process. This paper presents measurement data obtained under laboratory conditions as well as the results obtained by establishing a virtual QKD link. Despite the common beliefs that increased quantum bit error rate implies a larger amount of traffic on the public channel, our measurements prove the opposite. The obtained data clearly show that the public channel has a major impact on the overall performance of the QKD link.

Implementation of quantum key distribution network simulation module in the network simulator NS-3

As the research in quantum key distribution (QKD) technology grows larger and becomes more complex, the need for highly accurate and scalable simulation technologies becomes important to assess the practical feasibility and foresee difficulties in the practical implementation of theoretical achievements. Due to the specificity of the QKD link which requires optical and Internet connection between the network nodes, to deploy a complete testbed containing multiple network hosts and links to validate and verify a certain network algorithm or protocol would be very costly. Network simulators in these circumstances save vast amounts of money and time in accomplishing such a task. The simulation environment offers the creation of complex network topologies, a high degree of control and repeatable experiments, which in turn allows researchers to conduct experiments and confirm their results. In this paper, we described the design of the QKD network simulation module which was developed in the network simulator of version 3 (NS-3). The module supports simulation of the QKD network in an overlay mode or in a single TCP/IP mode. Therefore, it can be used to simulate other network technologies regardless of QKD.

Experimental demonstration of kilometer-range quantum digital signatures

We present an experimental realization of a quantum digital signature protocol which, together with a standard quantum key distribution link, increases transmission distance to kilometre ranges, three orders of magnitude larger than in previous realizations. The bit-rate is also significantly increased compared with previous quantum signature demonstrations. This work illustrates that quantum digital signatures can be realized with optical components similar to those used for quantum key distribution, and could be implemented in existing optical fiber networks.

Long-Distance Trust-Free Quantum Key Distribution

The feasibility of trust-free long-haul quantum key distribution (QKD) is addressed. We combine measurement-device-independent QKD, as an access technology, with a quantum repeater setup, at the core of future quantum communication networks. This will provide a quantum link none of whose intermediary nodes need to be trusted, or, in our terminology, a trust-free QKD link. As the main figure of merit, we calculate the secret key generation rate when a particular probabilistic quantum repeater protocol is in use. We assume the users are equipped with imperfect single photon sources, which can possibly emit two single photons, or laser sources to implement decoy-state techniques. We consider apparatus imperfection, such as quantum efficiency and dark count of photodetectors, path loss of the channel, and writing and reading efficiencies of quantum memories. By optimizing different system parameters, we estimate the maximum distance over which users can share secret keys when a finite number of memories are employed in the repeater setup.