Unconditional security of quantum key distribution over arbitrarily long distances

Experimental quantum Byzantine agreement on a three-user quantum network with integrated photonics

Quantum communication networks are crucial for both secure communication and cryptographic networked tasks. Building quantum communication networks in a scalable and cost-effective way is essential for their widespread adoption. Here, we establish a complete polarization entanglement-based fully connected network, which features an ultrabright integrated Bragg reflection waveguide quantum source, managed by an untrusted service provider, and a streamlined polarization analysis module, which requires only one single-photon detector for each user. We perform a continuously working quantum entanglement distribution and create correlated bit strings between users. Within the framework of one-time universal hashing, we provide the experimental implementation of source-independent quantum digital signatures using imperfect keys circumventing the necessity for private amplification. We further beat the 1/3 fault tolerance bound in the Byzantine agreement, achieving unconditional security without relying on sophisticated techniques. Our results offer an affordable and practical route for addressing consensus challenges within the emerging quantum network landscape.

Metal-Organic Frameworks (MOFs): Classification, Synthesis, Modification, and Biomedical Applications

Metal-organic frameworks (MOFs) are a new variety of solid crystalline porous functional materials. As an extension of inorganic porous materials, it has made important progress in preparation and application. MOFs are widely used in various fields such as gas adsorption storage, drug delivery, sensing, and biological imaging due to their high specific surface area, porosity, adjustable pore size, abundant active sites, and functional modification by introducing groups. In this paper, the types of MOFs are classified, and the synthesis methods and functional modification mechanisms of MOFs materials are summarized. Finally, the application prospects and challenges of metal-organic framework materials in the biomedical field are discussed, hoping to promote their application in multidisciplinary fields.

Optimal and scalable entanglement distribution over crossbar quantum networks

Crossbar networks are a cornerstone of network architectures, capable of operating both as standalone interconnections or as integral switching components in complex, multi-stage systems. The main advantages of crossbar networks are their non-blocking operation and unparalleled minimal latency. With the advent of large scale quantum networks, crossbars might be an important asset towards the Quantum Internet. This study proposes a solution for the problem of distributing entanglement within crossbar quantum networks. Entangled particles are a consumable resource in quantum networks, and are being used by most quantum protocols. By ensuring that nodes within quantum networks are being supplied with entanglement, the reliability and efficiency of the network is maintained. By providing an efficient, scalable framework that can be used to achieve optimal entanglement distribution within crossbar quantum networks, this study offers a theoretical achievement which can be also used for enhancing quantum network performance. An algorithm for selecting an optimal entanglement distribution configuration is proposed and fully tested on realistic possible configurations.

Enhancing the performance of mode-pairing quantum key distribution by wavelength division multiplexing

Mode-pairing quantum key distribution (MP-QKD) holds great promise for the practical implementation of QKD in the near future. It combines the security advantages of measurement device independence while still being capable of breaking the Pirandola-Laurenza-Ottaviani-Banchi bound without the need for highly demanding phase-locking and phase-tracking technologies for deployment. In this work, we explore optimization strategies for MP-QKD in a wavelength-division multiplexing scenario. The simulation results reveal that incorporation of multiple wavelengths not only leads to a direct increase in key rate but also enhances the pairing efficiency by employing our novel pairing strategies among different wavelengths. As a result, our work provides a new avenue for the future application and development of MP-QKD.

Reduction-Induced Uptake of Cs+ in Metal-Organic Frameworks Loaded with Polyoxometalates

Materials for Cs+ adsorption continue to be important for the treatment of various solutions. Metal-organic frameworks (MOFs) with large specific surface areas promise adsorption properties for various gases, vapors, and ions. However, the utilization of MOFs for alkali ion capture, specifically, Cs+ capture is still in its infancy. Herein, MOFs are hybridized with polyoxometalates (POMs) to study the effect of i) MOF type, ii) POM type, and iii) POM loading amounts on Cs+ capture. In particular, the composite of ZIF-8 and [α-PMo12 O40 ]3- (PMo12 /ZIF-8) adsorbed Cs+ ions effectively when compared to pristine ZIF-8. In addition, the reduction of Mo within the POM from MoVI to MoV by ascorbic acid during the Cs+ uptake process doubled the Cs+ uptake capacity of PMo12 /ZIF-8. This observation can be attributed to the increased overall negative charge of the POM facilitating Cs+ uptake to compensate for the charge imbalance. Hybridization with other MOFs (MIL-101 and UiO-66) largely suppresses the Cs+ uptake, highlighting the importance of hydrophobicity in Cs+ capture. Furthermore, PMo12 /ZIF-8 led to an outstanding Cs+ uptake (291.5 mg g-1 ) with high selectivity (79.6%) from quinary mixtures of alkali metal cations even among other representative porous materials (Prussian blue and zeolites).

Robust frame synchronization for continuous-variable quantum key distribution with coherent states

In a practical continuous variable quantum key distribution (CVQKD) system, frame synchronization is crucial for its operation, especially in conditions of low signal-to-noise ratio (SNR) and phase drift. This paper introduces a robust frame synchronization scheme for CVQKD systems that only utilizes quantum signals. The proposed scheme effectively employs randomly selected segments of quantum signals to achieve frame synchronization, eliminating the need for additional modulation. The performance of this scheme applied in a local local oscillator scenario is thoroughly analyzed through numerical simulations. The results demonstrate that the proposed scheme is capable of withstanding low SNR and arbitrary slow phase drift, as well as fast phase drift originates from two independent lasers, while also slightly improving the secret key rate compared to the scheme using inserted synchronization frames. These findings validate the feasibility of implementing the proposed scheme for long-distance CVQKD in practical scenarios.

Electrocatalytic CO2 Reduction to Ethylene: From Advanced Catalyst Design to Industrial Applications

The value-added chemicals, monoxide, methane, ethylene, ethanol, ethane, and so on, can be efficiently generated through the electrochemical CO2 reduction reaction (eCO2 RR) when equipped with suitable catalysts. Among them, ethylene is particularly important as a chemical feedstock for petrochemical manufacture. However, despite its high Faradaic efficiency achievable at relatively low current densities, the substantial enhancement of ethylene selectivity and stability at industrial current densities poses a formidable challenge. To facilitate the industrial implementation of eCO2 RR for ethylene production, it is imperative to identify key strategies and potential solutions through comprehending the recent advancements, remaining challenges, and future directions. Herein, the latest and innovative catalyst design strategies of eCO2 RR to ethylene are summarized and discussed, starting with the properties of catalysts such as morphology, crystalline, oxidation state, defect, composition, and surface engineering. The review subsequently outlines the related important state-of-the-art technologies that are essential in driving forward eCO2 RR to ethylene into practical applications, such as CO2 capture, product separation, and downstream reactions. Finally, a greenhouse model that integrates CO2 capture, conversion, storage, and utilization is proposed to present an ideal perspective direction of eCO2 RR to ethylene.

Security of the Decoy-State BB84 Protocol with Imperfect State Preparation

The quantum key distribution (QKD) allows two remote users to share a common information-theoretic secure secret key. In order to guarantee the security of a practical QKD implementation, the physical system has to be fully characterized and all deviations from the ideal protocol due to various imperfections of realistic devices have to be taken into account in the security proof. In this work, we study the security of the efficient decoy-state BB84 QKD protocol in the presence of the source flaws, caused by imperfect intensity and polarization modulation. We investigate the non-Poissonian photon-number statistics due to coherent-state intensity fluctuations and the basis-dependence of the source due to non-ideal polarization state preparation. The analysis is supported by the experimental characterization of intensity and phase distributions.

Metasurfaces for generating higher-order Poincaré beams by polarization-selective focusing and overall elimination of co-polarization components

Focused higher-order Poincaré (HOP) beams are of particular interest because they facilitate understanding the exotic properties of structured light and their applications in classical physics and quantum information. However, generating focused HOP beams using metasurfaces is challenging. In this study, we proposed a metasurface design comprising two sets of metal nanoslits for generating coaxially focused HOP beams. The nanoslits were interleaved on equispaced alternating rings. The initial rings started at the two adjacent Fresnel zones to provide opposite propagation phases for overall elimination of the co-polarization components. With the designed hyperbolic and helical profiles of the geometric phases, the two vortices of the opposite cross-circular-polarizations were formed and selectively focused, realizing HOP beams of improved quality. Simulations and experimental results demonstrated the feasibility of the proposed metasurface design. This study is of significance in the integration of miniaturized optical devices and enriches the application areas of metasurfaces.

Quantum-aided secure deep neural network inference on real quantum computers

Deep neural networks (DNNs) are phenomenally successful machine learning methods broadly applied to many different disciplines. However, as complex two-party computations, DNN inference using classical cryptographic methods cannot achieve unconditional security, raising concern on security risks of DNNs' application to sensitive data in many domains. We overcome such a weakness by introducing a quantum-aided security approach. We build a quantum scheme for unconditionally secure DNN inference based on quantum oblivious transfer with an untrusted third party. Leveraging DNN's noise tolerance, our approach enables complex DNN inference on comparatively low-fidelity quantum systems with limited quantum capacity. We validated our method using various applications with a five-bit real quantum computer and a quantum simulator. Both theoretical analyses and experimental results demonstrate that our approach manages to operate on existing quantum computers and achieve unconditional security with a negligible accuracy loss. This may open up new possibilities of quantum security methods for deep learning.

Quantum Complementarity Approach to Device-Independent Security

Complementarity is an essential feature of quantum mechanics. The preparation of an eigenstate of one observable implies complete randomness in its complementary observable. In quantum cryptography, complementarity allows us to formulate security analyses in terms of phase-error correction. However, the concept becomes much subtler in the device-independent regime that offers security without device characterization. Security proofs of device-independent quantum cryptography tasks are often complex and quite different from those of their more standard device-dependent cousins. The existing proofs pose huge challenges to experiments, among which large data-size requirement is a crux. Here, we show the complementarity security origin of the device-independent tasks. By linking complementarity with quantum nonlocality, we recast the device-independent scheme into a quantum error correction protocol. Going beyond the identical-and-independent-distribution case, we consider the most general attack. We generalize the sample entropy in classical Shannon theory for the finite-size analysis. Our method exhibits good finite-size performance and brings the device-independent scheme to a more practical regime. Applying it to the data in a recent ion-trap-based device-independent quantum key distribution experiment, one could reduce the requirement on data size to less than a third. Furthermore, the operational meaning of complementarity naturally extends device-independent scenarios to advantage key distillation, easing experiments by tolerating higher loss and lower transmittance.

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.

Security of quantum key distribution from generalised entropy accumulation

The goal of quantum key distribution (QKD) is to establish a secure key between two parties connected by an insecure quantum channel. To use a QKD protocol in practice, one has to prove that a finite size key is secure against general attacks: no matter the adversary's attack, they cannot gain useful information about the key. A much simpler task is to prove security against collective attacks, where the adversary is assumed to behave identically and independently in each round. In this work, we provide a formal framework for general QKD protocols and show that for any protocol that can be expressed in this framework, security against general attacks reduces to security against collective attacks, which in turn reduces to a numerical computation. Our proof relies on a recently developed information-theoretic tool called generalised entropy accumulation and can handle generic prepare-and-measure protocols directly without switching to an entanglement-based version.

Non-classical correlations of accelerated observers interacting with a classical stochastic noise beyond the single mode approximation

This paper investigates the behaviour of the quantum correlations for an accelerated two-qubit system during its interaction with a classical stochastic field, utilizing the Wigner function and concurrence. The non-classical behaviour is indicated by negative values of the Wigner function, while the degree of entanglement is demonstrated by the concurrence. To consider acceleration and interaction with a common or independent environment, we discard the single-mode approximation and utilize the Unruh construction of the quantum field mode in our analysis. Our results suggest that coherence suppression is caused by the acceleration effect, noise strength, and noise frequency. Through an examination of quantum concurrence, this study analyses the level of quantum entanglement that corresponds positively with negative values of the Wigner function. The findings indicate that coherence degradation in the initial system is reduced when observers interact independently with their environments, as opposed to interacting with a common environment. Additionally, the acceleration of both observers has an impact on coherence reduction. During system evolution, the Wigner function displays collapse and reappearance behaviour, while quantum entanglement undergoes local collapse and revival phenomena. Notably, common noise situations exhibit more rapid variation in both the Wigner function and entanglement compared to independent noise configurations.

Topology Abstraction-Based Routing Scheme for Secret-Key Provisioning in Hybrid GEO/LEO Quantum Satellite Networks

Quantum key distribution (QKD) is a promising technique to resist the threat against quantum computers. However, the high loss of quantum signals over a long-distance optical fiber is an obstacle for QKD in the intercontinental domain. In this context, the quantum satellite network is preferred over the terrestrial quantum optical network. Due to the mobility of satellites, the satellite topology is dynamic in the quantum satellite network, which remains a challenge for routing. In hybrid geostationary-earth-orbit (GEO)/low-earth-orbit (LEO) quantum satellite networks, the lack of an efficient scheduling scheme for GEO/LEO satellites also limits the construction of quantum satellite networks. Therefore, this paper provides a topology abstraction-based routing scheme for secret-key provisioning, where the dynamic physical topology is translated into a quasi-static abstracted topology. This scheme contributes to saving the precious secret key resources. In order to improve the success probability of long-distance QKD requests, three novel resource-scheduling heuristic algorithms are proposed in hybrid GEO/LEO quantum satellite networks. Simulation results indicate that the proposed algorithms can improve the success probability of QKD requests by 47% compared to the benchmark.

Effects of experimental impairments on the security of continuous-variable quantum key distribution

Quantum Key Distribution (QKD) is a cutting-edge communication method that enables secure communication between two parties. Continuous-variable QKD (CV-QKD) is a promising approach to QKD that has several advantages over traditional discrete-variable systems. Despite its potential, CV-QKD systems are highly sensitive to optical and electronic component impairments, which can significantly reduce the secret key rate. In this research, we address this challenge by modeling a CV-QKD system to simulate the impact of individual impairments on the secret key rate. The results show that laser frequency drifts and small imperfections in electro-optical devices such as the beam splitter and the balanced detector have a negative impact on the secret key rate. This provides valuable insights into strategies for optimizing the performance of CV-QKD systems and overcome limitations caused by component impairments. By offering a method to analyze them, the study enables the establishment of quality standards for the components of CV-QKD systems, driving the development of advanced technologies for secure communication in the future.

Measurement-Device-Independent Quantum Key Distribution Based on Decoherence-Free Subspaces with Logical Bell State Analyzer

Measurement-device-independent quantum key distribution (MDI-QKD) enables two legitimate users to generate shared information-theoretic secure keys with immunity to all detector side attacks. However, the original proposal using polarization encoding is sensitive to polarization rotations stemming from birefringence in fibers or misalignment. To overcome this problem, here we propose a robust QKD protocol without detector vulnerabilities based on decoherence-free subspaces using polarization-entangled photon pairs. A logical Bell state analyzer is designed specifically for such encoding. The protocol exploits common parametric down-conversion sources, for which we develop a MDI-decoy-state method, and requires neither complex measurements nor a shared reference frame. We have analyzed the practical security in detail and presented a numerical simulation under various parameter regimes, showing the feasibility of the logical Bell state analyzer along with the potential that double communication distance can be achieved without a shared reference frame.

A Resource-Adaptive Routing Scheme with Wavelength Conflicts in Quantum Key Distribution Optical Networks

Quantum key distribution (QKD) has great potential in ensuring data security. Deploying QKD-related devices in existing optical fiber networks is a cost-effective way to practically implement QKD. However, QKD optical networks (QKDON) have a low quantum key generation rate and limited wavelength channels for data transmission. The simultaneous arrival of multiple QKD services may also lead to wavelength conflicts in QKDON. Therefore, we propose a resource-adaptive routing scheme (RAWC) with wavelength conflicts to achieve load balancing and efficient utilization of network resources. Focusing on the impact of link load and resource competition, this scheme dynamically adjusts the link weights and introduces the wavelength conflict degree. Simulation results indicate that the RAWC algorithm is an effective approach to solving the wavelength conflict problem. Compared with the benchmark algorithms, the RAWC algorithm can improve service request success rate (SR) by up to 30%.

Experimental free-space continuous-variable quantum key distribution with thermal source

Passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) protocol explores the intrinsic field fluctuations of a thermal source. Compared with traditional Gaussian-modulated coherent-state CVQKD, it does not need active modulations and has promising applications in chip integration and portable free-space quantum key distribution. In this Letter, we propose and experimentally realize a PSP CVQKD scheme with transmitted local oscillator (LO) through fluctuating transmittance free-space channel using an off-the-shelf amplified spontaneous emission source for the first time. By proposing thermal-state polarization multiplexing transmitted LO, synchronized channel transmittance monitoring and fine-grained phase compensation techniques, secure keys within -15 dB transmittance of simulated free-space channel with turbulence are generated, with a final average secure key rate of 1.015 Mbps asymptotically. Equivalent atmospheric turbulence model analysis shows that the free-space PSP CVQKD scheme provides a promising outlook for high-speed and chip-based CVQKD for kilometer-level atmospheric channel networks.

Small-form-factor Gaussian-modulated coherent-state transmitter for CV-QKD using a gain-switched DFB laser

We report a directly modulated distributed feedback laser operating in gain-switching mode for preparing the coherent states required for the Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) protocol. The proposed single-component quantum transmitter design eliminates the need for external modulators, decreasing the complexity of GMCS CV-QKD systems. The experimental results demonstrate a potential asymptotic secret key rate value of 2.63 Mbps over an 11-km fiber link, making the directly modulated GMCS transmitter particularly suitable for metropolitan optical networks where compactness, robustness, and low cost are key desirable features.

Finite-Key Analysis for Quantum Key Distribution with Discrete-Phase Randomization

Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2π, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,π/4,π/2,…,7π/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.

Experimental Mode-Pairing Measurement-Device-Independent Quantum Key Distribution without Global Phase Locking

In the past two decades, quantum key distribution networks based on telecom fibers have been implemented on metropolitan and intercity scales. One of the bottlenecks lies in the exponential decay of the key rate with respect to the transmission distance. Recently proposed schemes mainly focus on achieving longer distances by creating a long-arm single-photon interferometer over two communication parties. Despite their advantageous performance over long communication distances, the requirement of phase locking between two remote lasers is technically challenging. By adopting the recently proposed mode-pairing idea, we realize high-performance quantum key distribution without global phase locking. Using two independent off-the-shelf lasers, we show a quadratic key-rate improvement over the conventional measurement-device-independent schemes in the regime of metropolitan and intercity distances. For longer distances, we also boost the key rate performance by 3 orders of magnitude via 304 km commercial fiber and 407 km ultralow-loss fiber. We expect this ready-to-implement high-performance scheme to be widely used in future intercity quantum communication networks.

Encryption chain based on measurement result and its applications on semi-quantum key distribution protocol

This study proposes a new encoding method, also known as an encryption chain based on the measurement result. Then, using the encryption chain to propose a unitary-operation-based semi-quantum key distribution protocol (SQKD) protocol. In the existing SQKD protocols, semi-quantum environments adopt a round-trip transmission strategy. In round-trip transmission, the classical participant must resend the received photons to the quantum participant after implementing local operations. Therefore, round-trip transmissions are vulnerable to Trojan horse attacks. Hence, the classical participant must be equipped with a photon number splitter and an optical wavelength filter device against Trojan horse attacks. This is illogical for semi-quantum environments because the burden on the classical participant is significantly increased as it involves the prevention of Trojan horse attacks. The proposed SQKD protocol is congenitally immune to Trojan horse attacks and involves no extra hardware because it is designed based on a one-way transmission as opposed to a round-trip transmission. When compared to the existing SQKD protocols, the proposed SQKD protocol provides the best qubit efficiency, and classical participants only require two quantum capabilities, which enhance its practicability. Moreover, the proposed SQKD protocol is free from collective attacks, Trojan horse attacks, and intercept-resend attacks. Thus, the proposed scheme is more efficient and practical than the existing SQKD protocols.

Advances in Chip-Based Quantum Key Distribution

Quantum key distribution (QKD), guaranteed by the principles of quantum mechanics, is one of the most promising solutions for the future of secure communication. Integrated quantum photonics provides a stable, compact, and robust platform for the implementation of complex photonic circuits amenable to mass manufacture, and also allows for the generation, detection, and processing of quantum states of light at a growing system's scale, functionality, and complexity. Integrated quantum photonics provides a compelling technology for the integration of QKD systems. In this review, we summarize the advances in integrated QKD systems, including integrated photon sources, detectors, and encoding and decoding components for QKD implements. Complete demonstrations of various QKD schemes based on integrated photonic chips are also discussed.

Quantum Zeno repeaters

Quantum repeaters pave the way for long-distance quantum communications and quantum Internet, and the idea of quantum repeaters is based on entanglement swapping which requires the implementation of controlled quantum gates. Frequently measuring a quantum system affects its dynamics which is known as the quantum Zeno effect (QZE). Beyond slowing down its evolution, QZE can be used to control the dynamics of a quantum system by introducing a carefully designed set of operations between measurements. Here, we propose an entanglement swapping protocol based on QZE, which achieves almost unit fidelity. Implementation of our protocol requires only simple frequent threshold measurements and single particle rotations. We extend the proposed entanglement swapping protocol to a series of repeater stations for constructing quantum Zeno repeaters which also achieve almost unit fidelity regardless of the number of repeaters. Requiring no controlled gates, our proposal reduces the quantum circuit complexity of quantum repeaters. Our work has potential to contribute to long distance quantum communications and quantum computing via quantum Zeno effect.

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user's pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method.

Post-matching quantum conference key agreement

Twin-field interference-based quantum conference key agreement protocols have been proposed and have achieved good performance in terms of the key rate and transmission distance in the finite-key regime. However, its performance significantly decreases when the strict constraint is broken regarding the optical pulse intensity and probability. Here, we propose a post-matching QCKA protocol to remove this constraint while obtaining a higher key rate. Numerical results in the symmetric case show that our protocol can obtain a transmission distance 25% more than the previous asymmetric QCKA protocol when the decoy state optical pulse intensity is 1% higher than the ideal value of the constraint, and can obtain a transmission distance 100% higher when the decoy state optical pulse intensity is 10% higher than the ideal value of the constraint.

Toward a Photonic Demonstration of Device-Independent Quantum Key Distribution

The security of quantum key distribution (QKD) usually relies on that the users' devices are well characterized according to the security models made in the security proofs. In contrast, device-independent QKD-an entanglement-based protocol-permits the security even without any knowledge of the underlying quantum devices. Despite its beauty in theory, device-independent QKD is elusive to realize with current technologies. Especially in photonic implementations, the requirements for detection efficiency are far beyond the performance of any reported device-independent experiments. In this Letter, we report a proof-of-principle experiment of device-independent QKD based on a photonic setup in the asymptotic limit. On the theoretical side, we enhance the loss tolerance for real device imperfections by combining different approaches, namely, random postselection, noisy preprocessing, and developed numerical methods to estimate the key rate via the von Neumann entropy. On the experimental side, we develop a high-quality polarization-entangled photon source achieving a state-of-the-art (heralded) detection efficiency about 87.5%. Although our experiment does not include random basis switching, the achieved efficiency outperforms previous photonic experiments involving loophole-free Bell tests. Together, we show that the measured quantum correlations are strong enough to ensure a positive key rate under the fiber length up to 220 m. Our photonic platform can generate entangled photons at a high rate and in the telecom wavelength, which is desirable for high-speed generation over long distances. The results present an important step toward a full demonstration of photonic device-independent QKD.

Authentication of smart grid communications using quantum key distribution

Smart grid solutions enable utilities and customers to better monitor and control energy use via information and communications technology. Information technology is intended to improve the future electric grid’s reliability, efficiency, and sustainability by implementing advanced monitoring and control systems. However, leveraging modern communications systems also makes the grid vulnerable to cyberattacks. Here we report the first use of quantum key distribution (QKD) keys in the authentication of smart grid communications. In particular, we make such demonstration on a deployed electric utility fiber network. The developed method was prototyped in a software package to manage and utilize cryptographic keys to authenticate machine-to-machine communications used for supervisory control and data acquisition (SCADA). This demonstration showcases the feasibility of using QKD to improve the security of critical infrastructure, including future distributed energy resources (DERs), such as energy storage.

Mode-pairing quantum key distribution

Quantum key distribution — the establishment of information-theoretically secure keys based on quantum physics — is mainly limited by its practical performance, which is characterised by the dependence of the key rate on the channel transmittance R(η). Recently, schemes based on single-photon interference have been proposed to improve the key rate to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=O(\sqrt{\eta })$$\end{document}R=O(η) by overcoming the point-to-point secret key capacity bound with interferometers. Unfortunately, all of these schemes require challenging global phase locking to realise a stable long-arm single-photon interferometer with a precision of approximately 100 nm over fibres that are hundreds of kilometres long. Aiming to address this problem, we propose a mode-pairing measurement-device-independent quantum key distribution scheme in which the encoded key bits and bases are determined during data post-processing. Using conventional second-order interference, this scheme can achieve a key rate of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R=O(\sqrt{\eta })$$\end{document}R=O(η) without global phase locking when the local phase fluctuation is mild. We expect this high-performance scheme to be ready-to-implement with off-the-shelf optical devices.

Measurement-device-independent QKD schemes suffer from a trade-off between ease of implementation (avoiding the need for global phase locking) and high rates (quadratic improvement in rate). Here, the authors propose a protocol which offers both simple implementation and strong performances.

Imperfection-insensitivity quantum random number generator with untrusted daily illumination

Quantum random number generators (QRNGs) promise secure randomness generation based on the foundational unpredictability of quantum mechanics. However, the unavoidable gaps between theoretical models and practical devices could lead to security invalidation. Recently, a source-independent quantum random number generator (SI-QRNG) has been proposed to solve the issue of uncharacteristic sources. However, in most current analyses of SI-QRNG protocols, the security proofs with imperfect measurements are individual for different factors and very sensitive to small deviations from theoretical models. Here, we establish a unified model for imperfect measurements in the SI-QRNG and provide a tight rate bound based on the uncertainty relation for smooth entropies. Then the performance with large device imperfections is evaluated and the randomness rate in our model can approach a similar order of magnitude of the rate upper bound in common discrete variable QRNGs. In addition, by utilizing the daily illumination and measurement devices with large imperfections, we experimentally demonstrate our scheme at the rate of the order of magnitude of Mbps.

Improved polar-code-based efficient post-processing algorithm for quantum key distribution

Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and the wiretap channel respectively under the Wyner's wiretap channel model, we design a codeword structure of polar codes, so that the error correction and privacy amplification could be completed synchronously in a single step. Through combining error correction and privacy amplification into one single step, this efficient post-processing algorithm reduces complexity of the system and lower the post-processing delay. Besides, the reliable and secure communicaiton conditions for this algorithm has been given in this paper. Simulation results show that this post-processing algorithm satisfies the reliable and secure communication conditions well.

Practical underwater quantum key distribution based on decoy-state BB84 protocol

Polarization encoding quantum key distribution has been proven to be a reliable method to build a secure communication system. It has already been used in an inter-city fiber channel and near-Earth atmosphere channel, leaving an underwater channel the last barrier to conquer. Here we demonstrate a decoy-state BB84 quantum key distribution system over a water channel with a compact system design for future experiments in the ocean. In the system, a multiple-intensity modulated laser module is designed to produce the light pulses of quantum states, including signal state, decoy state, and vacuum state. Classical communication and synchronization are realized by wireless optical transmission. Multiple filtering techniques and wavelength division multiplexing are further used to avoid cross talk of different lights. We test the performance of the system and obtain a final key rate of 245.6 bps with an average quantum bit error rate of 1.91% over a 2.4 m water channel, in which the channel attenuation is 16.35 dB. Numerical simulation shows that the system can tolerate up to 21.7 dB total channel loss and can still generate secure keys in 277.9 m Jerlov type I ocean channel.

Sending-or-Not-Sending Twin-Field Quantum Key Distribution with a Passive Decoy-State Method

Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because it can exceed the basic rate-distance limit without quantum repeaters. Its variant protocol, sending or not-sending quantum key distribution (SNS-QKD), not only fixes the security vulnerability of TF-QKD, but also can tolerate large misalignment errors. However, the current SNS-QKD protocol is based on the active decoy-state method, which may lead to side channel information leakage when multiple light intensities are modulated in practice. In this work, we propose a passive decoy-state SNS-QKD protocol to further enhance the security of SNS-QKD. Numerical simulation results show that the protocol not only improves the security in source, but also retains the advantages of tolerating large misalignment errors. Therefore, it may provide further guidance for the practical application of SNS-QKD.

Strong Coupling between a Single Quantum Emitter and a Plasmonic Nanoantenna on a Metallic Film

The strong coupling between single quantum emitters and resonant optical micro/nanocavities is beneficial for understanding light and matter interactions. Here, we propose a plasmonic nanoantenna placed on a metal film to achieve an ultra-high electric field enhancement in the nanogap and an ultra-small optical mode volume. The strong coupling between a single quantum dot (QD) and the designed structure is investigated in detail by both numerical simulations and theoretical calculations. When a single QD is inserted into the nanogap of the silver nanoantenna, the scattering spectra show a remarkably large splitting and anticrossing behavior of the vacuum Rabi splitting, which can be achieved in the scattering spectra by optimizing the nanoantenna thickness. Our work shows another way to enhance the light/matter interaction at a single quantum emitter limit, which can be useful for many nanophotonic and quantum applications.

Passive Light Source Monitoring for Sending or Not Sending Twin-Field Quantum Key Distribution

Twin-field quantum key distribution (TF-QKD) can break the repeaterless linear bound and possess the measurement-device-independent security, and thus seems very promising in practical applications of quantum secure communication. In most reported TF-QKD protocols, light sources are assumed to possess trusted and fixed photon number distributions (PND), which are unrealistic assumptions in practical applications. Fortunately, the light source monitoring (LSM) method is proposed to circumvent this problem by actively adjusting the attenuation coefficient and monitoring the photon number distribution of light sources. However, the active light source monitoring (ALSM) method may induce additional modulation errors due to imperfect attenuation devices, deteriorating practical performances of TF-QKD systems. In this manuscript, we propose a passive light source monitoring (PLSM) scheme for TF-QKD, and employ the sending-or-not-sending (SNS) TF-QKD as an example for illustration. Simulation results show that our present work can greatly exceed both the original SNS protocol and the ALSM scheme when light source fluctuations and modulation errors are taken into account.

Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation

Quantum cryptography is a well-stated field within quantum applications where quantum information is used to set secure communications, authentication, and secret keys. Now used in quantum devices with those purposes, particularly Quantum Key Distribution (QKD), which proposes a secret key between two parties free of effective eavesdropping, at least at a higher level than classical cryptography. The best-known quantum protocol to securely share a secret key is the BB84 one. Other protocols have been proposed as adaptations of it. Most of them are based on the quantum indeterminacy for non-orthogonal quantum states. Their security is commonly based on the large length of the key. In the current work, a BB84-like procedure for QKD based on double quantum teleportation allows the sharing of the key statement using several parties. Thus, the quantum bits of information are assembled among three parties via entanglement, instead of travelling through a unique quantum channel as in the traditional protocol. Asymmetry in the double teleportation plus post-measurement retains the secrecy in the process. Despite requiring more complex control and resources, the procedure dramatically reduces the probability of success for an eavesdropper under individual attacks, because of the ignorance of the processing times in the procedure. Quantum Bit Error Rate remains in the acceptable threshold and it becomes configurable. The article depicts the double quantum teleportation procedure, the associated control to introduce the QKD scheme, the analysis of individual attacks performed by an eavesdropper, and a brief comparison with other protocols.

Practical Security of High-Dimensional Quantum Key Distribution with Intensity Modulator Extinction

Quantum key distribution (QKD) has attracted much attention due to its unconditional security. High-dimensional quantum key distribution (HD-QKD) is a brand-new type of QKD protocol that has many excellent advantages. Nonetheless, practical imperfections in realistic devices that are not considered in the theoretical security proof may have an impact on the practical security of realistic HD-QKD systems. In this paper, we research the influence of a realistic intensity modulator on the practical security of HD-QKD systems with the decoy-state method and finite-key effects. We demonstrate that there is a certain impact in the secret key rate and the transmission distance when taking practical factors into security analysis.

Device-Independent Quantum Key Distribution with Random Postselection

Device-independent quantum key distribution (QKD) can permit the superior security even with unknown devices. In practice, however, the realization of device-independent QKD is technically challenging because of its low noise tolerance. In the photonic setup, due to the limited detection efficiency, a large amount of the data generates from no-detection events which contain few correlations but contribute high errors. Here, we propose the device-independent QKD protocol with random postselection, where the secret keys are extracted only from the postselected subset of outcomes. This could not open the detection loophole as long as the entropy of the postselected subset is evaluated from the information of the entire set of data, including both detection and no-detection events. This postselection has the advantage to significantly reduce the error events, thus relaxing the threshold of required detection efficiency. In the model of collective attacks, our protocol can tolerate detector efficiency as low as 68.5%, which goes beyond standard security proofs. The results make a concrete step for the implementation of device-independent QKD in practice.

Security Analysis of Continuous-Variable Measurement-Device-Independent Quantum Key Distribution Systems in Complex Communication Environments

Continuous-variable measure-device-independent quantum key distribution (CV-MDI QKD) is proposed to remove all imperfections originating from detection. However, there are still some inevitable imperfections in a practical CV-MDI QKD system. For example, there is a fluctuating channel transmittance in the complex communication environments. Here we investigate the security of the system under the effects of the fluctuating channel transmittance, where the transmittance is regarded as a fixed value related to communication distance in theory. We first discuss the parameter estimation in fluctuating channel transmittance based on these establishing of channel models, which has an obvious deviation compared with the estimated parameters in the ideal case. Then, we show the evaluated results when the channel transmittance respectively obeys the two-point distribution and the uniform distribution. In particular, the two distributions can be easily realized under the manipulation of eavesdroppers. Finally, we analyze the secret key rate of the system when the channel transmittance obeys the above distributions. The simulation analysis indicates that a slight fluctuation of the channel transmittance may seriously reduce the performance of the system, especially in the extreme asymmetric case. Furthermore, the communication between Alice, Bob and Charlie may be immediately interrupted. Therefore, eavesdroppers can manipulate the channel transmittance to complete a denial-of-service attack in a practical CV-MDI QKD system. To resist this attack, the Gaussian post-selection method can be exploited to calibrate the parameter estimation to reduce the deterioration of performance of the system.

A Verifiable Arbitrated Quantum Signature Scheme Based on Controlled Quantum Teleportation

In this paper, we present a verifiable arbitrated quantum signature scheme based on controlled quantum teleportation. The five-qubit entangled state functions as a quantum channel. The proposed scheme uses mutually unbiased bases particles as decoy particles and performs unitary operations on these decoy particles, applying the functional values of symmetric bivariate polynomial. As such, eavesdropping detection and identity authentication can both be executed. The security analysis shows that our scheme can neither be disavowed by the signatory nor denied by the verifier, and it cannot be forged by any malicious attacker.

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.

Fibre polarisation state compensation in entanglement-based quantum key distribution

Quantum key distribution (QKD) using polarisation encoding can be hard to implement over deployed telecom fibres because the routing geometry and the birefringence of the fibre link can alter the polarisation states of the propagating photons. These alterations cause a basis mismatch, leading to an increased quantum bit error rate (QBER). In this work we demonstrate a technique for a dynamically compensating fibre-induced state alteration in a QKD system. This compensation scheme includes a feedback loop that minimizes the QBER using a stochastic optimization algorithm. The effectiveness of this technique is implemented and verified in a polarisation entanglement QKD system over a deployed telecom fibre.

Quantum Plasmonics: Energy Transport Through Plasmonic Gap

At the interfaces of metal and dielectric materials, strong light-matter interactions excite surface plasmons; this allows electromagnetic field confinement and enhancement on the sub-wavelength scale. Such phenomena have attracted considerable interest in the field of exotic material-based nanophotonic research, with potential applications including nonlinear spectroscopies, information processing, single-molecule sensing, organic-molecule devices, and plasmon chemistry. These innovative plasmonics-based technologies can meet the ever-increasing demands for speed and capacity in nanoscale devices, offering ultrasensitive detection capabilities and low-power operations. Size scaling from the nanometer to sub-nanometer ranges is consistently researched; as a result, the quantum behavior of localized surface plasmons, as well as those of matter, nonlocality, and quantum electron tunneling is investigated using an innovative nanofabrication and chemical functionalization approach, thereby opening a new era of quantum plasmonics. This new field enables the ultimate miniaturization of photonic components and provides extreme limits on light-matter interactions, permitting energy transport across the extremely small plasmonic gap. In this review, a comprehensive overview of the recent developments of quantum plasmonic resonators with particular focus on novel materials is presented. By exploring the novel gap materials in quantum regime, the potential quantum technology applications are also searched for and mapped out.

Mitigating the effect of atmospheric turbulence on orbital angular momentum-based quantum key distribution using real-time adaptive optics with phase unwrapping

Quantum key distribution (QKD) employed orbital angular momentum (OAM) for high-dimensional encoding enhances the system security and information capacity between two communication parties. However, such advantagesare significantly degraded because of the fragility of OAM states in atmospheric turbulence. Unlike previous researches, we first investigate the performance degradation of OAM-based QKD by infinitely long phase screen (ILPS), which offers a feasible way to study how adaptive optics (AO) dynamically corrects the turbulence-induced aberrations in real time. Secondly, considering the failure of AO while encountering phase cuts, we evaluate the quality enhancement of OAM-based QKD under a moderate turbulence strength by AO after implementing the wrapped cuts elimination. Finally, we simulate that, with more realistic considerations; real-time AO can still mitigate the impact of atmospheric turbulence on OAM-based QKD even in the large wind velocity regime.

Influence of Source Parameters on the Polarization Properties of Beams for Practical Free-Space Quantum Key Distribution

Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens-Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.

Experimental measurement-device-independent quantum key distribution with the double-scanning method

The measurement-device-independent quantum key distribution (MDI-QKD) can be immune to all detector side-channel attacks. Moreover, it can be easily implemented combining with the matured decoy-state methods under current technology. It, thus, seems a very promising candidate in practical implementation of quantum communications. However, it suffers from a severe finite-data-size effect in most existing MDI-QKD protocols, resulting in relatively low key rates. Recently, Jiang et al. [Phys. Rev. A103, 012402 (2021).PLRAAN1050-294710.1103/PhysRevA.103.012402] proposed a double-scanning method to drastically increase the key rate of MDI-QKD. Based on Jiang et al.'s theoretical work, here we for the first time, to the best of our knowledge, implement the double-scanning method into MDI-QKD and carry out corresponding experimental demonstration. With a moderate number of pulses of 10¹⁰, we can achieve 150 km secure transmission distance, which is impossible with all former methods. Therefore, our present work paves the way toward practical implementation of MDI-QKD.

Multi-path-based quasi-real-time key provisioning in quantum-key-distribution enabled optical networks (QKD-ON)

With its information-theoretic security, quantum-key-distribution-enabled optical networks (QKD-ON) have become a promising candidate for future optical networks. The concept of quantum key pool (QKP) was introduced to offer an effective strategy for storing quantum keys. However, with the loss on its theoretical security due to storing these keys, balancing the storage of quantum keys and the security requirements of QKD-ONs poses a major challenge in their practical deployments. Hence, in this paper a concept of quasi-real-time key provisioning (QRT-KP) is introduced to address the tradeoff between quantum key storage and the degree of security. To satisfy the practical deployment of QRT-KP and the requirement of high-traffic flow, we propose a multi-path based QRT-KP (MP-QRT-KP) algorithm. Simulation results show that the MP-QRT-KP effectively enhances the performance of QKD-ONs in different scenarios, and it turns out that the algorithm performs better than single-path based QRT-KP (SP-QRT-KP) in terms of the success probability of key-allocation requests and key-resources utilization.

Demonstration of high-speed and low-complexity continuous variable quantum key distribution system with local local oscillator

We present an experimental demonstration of the feasibility of the first 20 + Mb/s Gaussian modulated coherent state continuous variable quantum key distribution system with a locally generated local oscillator at the receiver (LLO-CVQKD). To increase the signal repetition rate, and hence the potential secure key rate, we equip our system with high-performance, wideband devices and design the components to support high repetition rate operation. We have successfully trialed the signal repetition rate as high as 500 MHz. To reduce the system complexity and correct for any phase shift during transmission, reference pulses are interleaved with quantum signals at Alice. Customized monitoring software has been developed, allowing all parameters to be controlled in real-time without any physical setup modification. We introduce a system-level noise model analysis at high bandwidth and propose a new ‘combined-optimization’ technique to optimize system parameters simultaneously to high precision. We use the measured excess noise, to predict that the system is capable of realizing a record 26.9 Mb/s key generation in the asymptotic regime over a 15 km signal mode fibre. We further demonstrate the potential for an even faster implementation.