Quantum Key Distribution Research Articles

Security of AUV-carried OIRS-assisted quantum key distribution links in underwater channels subject to misalignment

To establish a secure and high-bandwidth communication link between the gateway node and the central node in the internet of underwater things (IoUwT), it is meaningful to introduce quantum key distribution (QKD) protocols into underwater wireless optical communication (UWOC) systems. However, the line-of-sight (LOS) requirement for photon transmission will pose an inevitable challenge to the QKD-based UWOC system. In this work, an optical intelligent reflecting surface (OIRS) array mounted on an autonomous underwater vehicle (AUV) is utilized for the first time to alleviate the LOS blockage and enable more reliable underwater wireless optical quantum link for both discrete-variable quantum key distribution (DV-QKD) and continuous-variable quantum key distribution (CV-QKD). To begin with, a novel statistical model of the aggregated channel transmissivity experienced by the OIRS-based quantum states in underwater link is derived by combing the effects of oceanic absorption, scattering, turbulence and OIRS misalignment, where the oceanic turbulence-induced irradiance fluctuation is modeled by exponential and generalized gamma (EGG) distribution, and the jitter angle associated with AUV-carried OIRS misalignment is characterized by a Rayleigh distribution. Then, on the basis of this statistical model and the Gauss-Chebyshev quadrature, the quantum bit error rate and the lower bound secret key rate (SKR) for the AUV-carried OIRS-assisted DV-QKD link are obtained with weak coherent optical source and decoy state idea by utilizing Gottesman-Lo-Lütkenhaus-Preskill. In terms of univariate Fox-H function, the average Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound over the bosonic pure-loss channel, as well as the thermal upper and lower bounds over the thermal-loss channel are both derived for the AUV-carried OIRS-assisted CV-QKD link. Additionally, the achievable SKR for a practical GG02 CV-QKD protocol in underwater channels is also presented through the worst-case analysis. Furthermore, the impacts of the number of OIRS elements, OIRS positioning, jitter variances, the probability of erroneous detection and link distance on the security performance of the proposed links are studied with different water types, thereby offering valuable insights for the QKD-based UWOC system in IoUwT.

Performance Improvement for Discretely Modulated Continuous-Variable Measurement-Device-Independent Quantum Key Distribution with Imbalanced Modulation

The modulation mode at the transmitters plays a crucial role in the continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) protocol. However, in practical applications, differences in the modulation schemes between two transmitters can inevitably impact protocol performance, particularly when using discrete modulation with four-state or eight-state formats. This work primarily investigates the effect of imbalanced modulation at the transmitters on the security of the CV-MDI-QKD protocol under both symmetric and asymmetric distance scenarios. By employing imbalanced discrete modulation maps and numerical convex optimization techniques, the proposed CV-MDI-QKD protocol achieves a notably higher secret key rate and outperforms existing protocols in terms of maximum transmission distance. Specifically, simulation results demonstrate that the secret key rate and maximum transmission distance are boosted by approximately 77.77% and 24.3%, respectively, compared to the original protocol. This novel and simplified modulation method can be seamlessly implemented in existing experimental setups without requiring equipment modifications. Furthermore, it provides a practical approach to enhancing protocol performance and enabling cost-effective applications in secure quantum communication networks under real-world environments.

A new control- and management architecture for SDN-enabled quantum key distribution networks

A new control- and management architecture for SDN-enabled quantum key distribution networks

Integrated InP-based Transmitter for Continuous-Variable Quantum Key Distribution

Integrated InP-based Transmitter for Continuous-Variable Quantum Key Distribution

How decoherence affects the security of BB84 quantum key distribution protocol

How decoherence affects the security of BB84 quantum key distribution protocol

Acoustic modulated passive planar lightwave circuit for quantum key distribution

Acoustic modulated passive planar lightwave circuit for quantum key distribution

Comparison of distributed and centralized quantum key management systems for meshed QKD networks

Recent developments in quantum key distribution (QKD) demonstrate the maturity of securing sensitive data against the emerging quantum computing threat. For QKD-secured long-haul and meshed optical transport networks (OTNs), quantum key management systems (QKMSs) are essential to overcome current distance limitations of available QKD devices. In this work, we present and compare two implementations of QKMSs, analyzing their scalability with an emulated QKD network (QKDN) utilizing recorded performance metrics from deployed QKD devices. First, we use a state-of-the-art Internet routing scheme, i.e., open shortest path first (OSPF), demonstrating that key management entities (KMEs) can solve the key routing problem utilizing distributed routing. Second, we apply software-defined networking (SDN) to implement centralized routing with a SDN controller. This paper compares distributed with centralized key routing regarding scalability, throughput, and latency. Both schemes facilitate up to six key relays between any pair of nodes in parallel with average key relay durations per hop below 300 ms given the Nobel-Germany topology and any-to-any demand matrix. With a network-wide joint key routing optimization in the SDN controller, up to 16.7% higher demands can be served compared to distributed key routing. Within the inherent compatibility of our study to network-function virtualization (NFV), we guideline future integration of QKMSs into deployed OTNs.

Memory-corrected quantum repeaters with adaptive syndrome identification

We address the challenge of incorporating encoded quantum memories into an exact secret key rate analysis for small and intermediate-scale quantum repeaters. To this end, we introduce the check matrix model and quantify the resilience of stabilizer codes of up to eleven qubits against Pauli noise, obtaining analytical expressions for effective logical error probabilities. Generally, we find that the five-qubit and Steane codes either outperform more complex, larger codes in the experimentally relevant parameter regimes or have a lower resource overhead. Subsequently, we apply our results to calculate lower bounds on the asymptotic secret key rate in memory-corrected quantum repeaters when using the five-qubit or Steane codes on the memory qubits. The five-qubit code drastically increases the effective memory coherence time, reducing a phase flip probability of 1% to 0.001% when employing an error syndrome identification adapted to the quantum noise channel. Furthermore, it mitigates the impact of faulty Bell state measurements and imperfect state preparation, lowering the minimally required depolarization parameter for nonzero secret key rates in an eight-segment repeater from 98.4% to 96.4%. As a result, the memory-corrected quantum repeater can often generate secret keys in experimental parameter regimes where the unencoded repeater fails to produce a secret key. In an eight-segment repeater, one can even achieve nonvanishing secret key rates up to distances of 2000 km for memory coherence times of tc=10 s or less using multiplexing. Assuming a zero-distance link-coupling efficiency p0=0.7, a depolarization parameter μ=0.99, tc=10 s, and an 800 km total repeater length, we obtain a secret key rate of 4.85 Hz, beating both the unencoded repeater that provides 1.25 Hz and ideal twin-field quantum key distribution with 0.71 Hz at GHz clock rates. Published by the American Physical Society 2025

High-dimensional coherent one-way quantum key distribution

High-dimensional quantum key distribution (QKD) offers secure communication with key rates that surpass those of QKD protocols utilizing two-dimensional encoding. However, existing high-dimensional QKD protocols require additional experimental resources, such as multiport interferometers and multiple detectors, thereby increasing the cost of high-dimensional systems and limiting their use. We introduce and analyze a high-dimensional QKD protocol that requires only standard two-dimensional hardware. We provide security analysis against individual and coherent attacks, establishing upper and lower bounds on the secure key rates. We tested our protocol on a standard two-dimensional QKD system over a 40 km fiber link, achieving a twofold increase in secure key rate compared to the standard two-dimensional coherent one-way protocol, without any hardware modifications. This work offers a significant improvement in the performance of already deployed QKD systems through simple software updates and holds broad applicability across various QKD schemes, making high-dimensional QKD practical for widespread use.

Quantum nonlocal modulation cancelation with distributed clocks

We demonstrate nonlocal modulation of entangled photons with truly distributed radio frequency (RF) clocks. Leveraging a custom radio-over-fiber (RFoF) system characterized via classical spectral interference, we validate its effectiveness for quantum networking by multiplexing the RFoF clock with one photon from a frequency-bin-entangled pair and distributing the coexisting quantum-classical signals over fiber. Phase modulation of the two photons reveals nonlocal correlations in excellent agreement with theory: in-phase modulation produces additional sidebands in the joint spectral intensity, while out-of-phase modulation is nonlocally canceled. Our simple, feedback-free design attains subpicosecond synchronization—namely, drift less than ∼0.5 ps in a 5.5 km fiber over 30 min (fractionally only ∼2×10−8 of the total fiber delay)—and should facilitate frequency-encoded quantum networking protocols such as high-dimensional quantum key distribution and entanglement swapping, unlocking frequency-bin qubits for practical quantum communications in deployed metropolitan-scale networks.

Wavelength Selection for Satellite Quantum Key Distribution

Current distance limitations of quantum key distribution (QKD) over fibre optic networks suggest that satellite (free-space optical) QKD networks will be required to enable global quantum communications. However, the operational availability of these systems is limited by background noise and strong attenuation caused by turbulence and adverse weather conditions. Using the decoy-state BB84 QKD protocol, we evaluate the secret key rate for a range of wavelengths, receiver sizes and initial beam waists through a variety of atmospheric conditions. We combine filtering techniques, adaptive optics, and wavelength selection to optimize the performance of satellite QKD. This study is simulation-based.

Simultaneous quantum identity authentication scheme utilizing entanglement swapping with secret key preservation

Unconditional security in Quantum Key Distribution (QKD) relies on authenticating the identities of users involved in key distribution. While classical identity authentication schemes were initially utilized in QKD implementations, concerns regarding their vulnerability have prompted the exploration of Quantum Identity Authentication (QIA) protocols. In this study, we introduce a new protocol for QIA, derived from the concept of controlled secure direct quantum communication. Our proposed scheme facilitates simultaneous authentication between two users, Alice and Bob, leveraging Bell states with the assistance of a third party, Charlie. Through rigorous security analysis, we demonstrate that the proposed protocol withstands various known attacks, including impersonation, intercept and resend and impersonated fraudulent attacks. Additionally, we establish the relevance of the proposed protocol by comparing it with the existing protocols of similar type.

A reconfigurable entanglement distribution network suitable for connecting multiple ground nodes with a satellite

Satellite-based quantum communication channels are important for ultra-long distances. Given the short duration of a satellite pass, it can be challenging to efficiently connect multiple users of a city-wide network while the satellite is passing over that area. We propose a network with dual-functionality: during a brief satellite pass, the ground network is configured as a multipoint-to-point topology where all ground nodes establish entanglement with a satellite receiver. During times when this satellite is not available, the satellite up-link is rerouted via a single optical switch to the ground nodes, and the network is configured as a pair-wise ground network. We numerically simulate a pulsed hyper-entangled photon source and study the performance of the proposed network configurations for quantum key distribution. We find favourable scaling in the case that the satellite receiver exploits time-multiplexing whereas the ground nodes utilize frequency-multiplexing. The scalability, simple reconfigurability, and easy integration with fibre networks make this architecture a promising candidate for quantum communication of many ground nodes and a satellite, an important step towards interconnection of ground nodes at a global scale.

Quantifying Quantum Steering with Limited Resources: A Semi‐supervised Machine Learning Approach

AbstractQuantum steering, an intermediate quantum correlation lying between entanglement and nonlocality, has emerged as a critical quantum resource for a variety of quantum information processing tasks such as quantum key distribution and true randomness generation. The ability to detect and quantify quantum steering is crucial for these applications. Semi‐definite programming (SDP) has proven to be a valuable tool to quantify quantum steering. However, the challenge lies in the fact that the optimal measurement strategy is not priori known, making it time‐consuming to compute the steerable measure for any given quantum state. Furthermore, the utilization of SDP requires full information of the quantum state, necessitating quantum state tomography, which can be complex and resource‐consuming. In this work, the semi‐supervised self‐training model is used to estimate the steerable weight, a pivotal measure of quantum steering. The model can be trained using a limited amount of labeled data, thus reducing the time for labeling. The features are constructed by the probabilities derived by performing three sets of projective measurements under arbitrary local unitary transformations on the target states, circumventing the need for quantum tomography. The model demonstrates robust generalization capabilities and can achieve high levels of precision with limited resources.

Practical security of twin-field quantum key distribution with optical phase-locked loop under wavelength-switching attack

The twin-field class quantum key distribution (TF-class QKD) has experimentally demonstrated the ability to surpass the fundamental rate-distance limit without requiring a quantum repeater, as a revolutional milestone. In TF-class QKD implementation, an optical phase-locked loop (OPLL) structure is commonly employed to generate a reference light with correlated phase, ensuring coherence of optical fields between Alice and Bob. In this configuration, the reference light, typically located in the untrusted station Charlie, solely provides wavelength reference for OPLL and does not participate in quantum-state encoding. However, the reference light may open a door for Eve to enter the source stations that are supposed to be well protected. Here, by identifying vulnerabilities of an acousto-optic modulator (AOM) in the OPLL scheme, we propose and demonstrate a wavelength-switching attack on a TF-class QKD system. This attack involves Eve deliberately manipulating the wavelength of the reference light to increase mean photon number of prepared quantum states, while maintaining stable interference between Alice and Bob as required by TF-class QKD protocols. The maximum observed increase in mean photon number is 8.7%, which has been theoretically proven to compromise the security of a TF-class QKD system. Moreover, we have shown that with well calibration of the modulators, the attack can be eliminated. Through this study, we highlight the importance of system calibration in the practical security in TF-class QKD implementation.

High-Performance Carrier Phase Recovery for Local Local Oscillator Continuous-Variable Quantum Key Distribution

High-Performance Carrier Phase Recovery for Local Local Oscillator Continuous-Variable Quantum Key Distribution

Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities

Maximum tolerable excess noise in continuous-variable quantum key distribution and improved lower bound on two-way capacities

Frequency-bin-encoded entanglement-based quantum key distribution in a reconfigurable frequency-multiplexed network

Large-scale quantum networks require dynamic and resource-efficient solutions to reduce system complexity with maintained security and performance to support growing number of users over large distances. Current encoding schemes including time-bin, polarization, and orbital angular momentum, suffer from the lack of reconfigurability and thus scalability issues. Here, we demonstrate the first-time implementation of frequency-bin-encoded entanglement-based quantum key distribution and a reconfigurable distribution of entanglement using frequency-bin encoding. Specifically, we demonstrate a novel scalable frequency-bin basis analyzer module that allows for a passive random basis selection as a crucial step in quantum protocols, and importantly equips each user with a single detector rather than four detectors. This minimizes massively the resource overhead, reduces the dark count contribution, vulnerability to detector side-channel attacks, and the detector imbalance, hence providing an enhanced security. Our approach offers an adaptive frequency-multiplexing capability to increase the number of channels without hardware overhead, enabling increased secret key rate and reconfigurable multi-user operations. In perspective, our approach enables dynamic resource-minimized quantum key distribution among multiple users across diverse network topologies, and facilitates scalability to large-scale quantum networks.

A Study on Security in Mode-Pairing and Sending-or-Not-Sending Quantum Key Distribution Protocols

In recent years, quantum key distribution (QKD) protocols have undergone rapid evolution, thus significantly advancing the field of quantum communications. The exploitation of quantum properties enables quantum communication to achieve superior security, yet many traditional protocols still face challenges in terms of stability and practicality. Since 2019, two new QKD protocols have emerged: mode-pairing QKD and sending-or-not-sending TF-QKD. In this paper, through an in-depth analysis of the existing literature, a simple mathematical derivation of the quantum uncertainty relation is provided, along with a systematic summary of the process for proving the security of these two new protocols. The results demonstrate that sending-or-not-sending TF-QKD can still effectively ensure the security of information in the presence of large bit error rates, showing its potential application in quantum communication. In addition, the paper explores future research directions, including experimental validation in diverse real-world environments, performance optimization, and the development of robust error correction techniques. These studies provide a critical foundation for the practicalization of QKD and promote the further development of quantum communication technology.

A Gray Image Quantum Encryption using GNEQR Representation

In the digital era, characterized by extensive online data exchange, information security has become a priority. While traditional encryption methods have proven effective in protecting data transfers, the advent of advanced quantum computing has increased susceptibility to security breaches. Quantum encryption provides a revolutionary solution to this problem by using quantum mechanics principles to establish algorithms that are impermeable to decryption. Using these quantum properties, cryptographic protocols are developed to provide superior security, unlike traditional encryption methods. The image plays an important role in transmitting information in all areas. Therefore, quantum image encryption methods are specifically designed to counter the potential risks posed by quantum computers, which can compromise conventional encryption protocols. This ensures the preservation of data security despite advances in quantum computing technology. In addition, quantum image encryption improves data transmission efficiency by establishing secure communication channels using quantum stats, thereby reducing the need for bandwidth and improving transmission speed. This paper proposes a new method of quantum encryption based on GNEQR representation and the modification of pixel values and positions in an image. After converting the image into a quantum form, we applied an algorithm to modify the values and positions of the pixels using a succession of quantum gates. We concluded this study with a statistical analysis showing the robustness of our quantum image encryption method.