Coherent states are increasingly being adopted for transmitting information in underwater quantum communications (UQCs). This paper presents what we believe to be a novel quantum multiple-symbol detection (QMSD) scheme designed to alleviate the performance degradation present in classical quantum symbol-by-symbol detection schemes, while operating without the need for channel state information (CSI) at the receiver. We model the communication system under the influence of an underwater channel and thermal noise at the receiver, and propose a novel QMSD metric based on positive operator-valued measure (POVM) quantum measurement results. Furthermore, we derive a closed-form expression for the QMSD metric for facilitating easy evaluation under marine turbulence conditions and thereby reducing implementation complexity. Using the simplified QMSD metric, we employ a sliding window algorithm to efficiently process the received quantum symbol sequence. Simulation results demonstrate that our proposed QMSD scheme enhances the quality of UQCs and exhibits robustness under marine turbulence conditions. Specifically, as the length of the detection sequence increases, the error probability of our scheme decreases. Moreover, as the average number of transmitted photons increases, the proposed QMSD scheme demonstrates superior performance, reducing error probability by 3 orders of magnitude compared to the quantum maximum likelihood detection (QMLD) scheme and by 5 orders of magnitude relative to the traditional homodyne detection (HD) scheme.
Coherent states are increasingly being adopted for transmitting information in underwater quantum communications (UQCs). This paper presents what we believe to be a novel quantum multiple-symbol detection (QMSD) scheme designed to alleviate the performance degradation present in classical quantum symbol-by-symbol detection schemes, while operating without the need for channel state information (CSI) at the receiver. We model the communication system under the influence of an underwater channel and thermal noise at the receiver, and propose a novel QMSD metric based on positive operator-valued measure (POVM) quantum measurement results. Furthermore, we derive a closed-form expression for the QMSD metric for facilitating easy evaluation under marine turbulence conditions and thereby reducing implementation complexity. Using the simplified QMSD metric, we employ a sliding window algorithm to efficiently process the received quantum symbol sequence. Simulation results demonstrate that our proposed QMSD scheme enhances the quality of UQCs and exhibits robustness under marine turbulence conditions. Specifically, as the length of the detection sequence increases, the error probability of our scheme decreases. Moreover, as the average number of transmitted photons increases, the proposed QMSD scheme demonstrates superior performance, reducing error probability by 3 orders of magnitude compared to the quantum maximum likelihood detection (QMLD) scheme and by 5 orders of magnitude relative to the traditional homodyne detection (HD) scheme.
Continuous-variable quantum key distribution (CV-QKD) is a promising approach for secure underwater quantum communications (UQCs), where propagation loss, scattering, turbulence, and receiver thermal noise can severely degrade the transmission of quantum states. In this paper, we propose an underwater CV-QKD system with virtual photon subtraction (VPS), implemented through post-selection of Alice's measurement outcomes, without requiring channel state information (CSI) at the receiver. Three VPS-based system configurations are analyzed, corresponding to homodyne detection (VPS-HD), quantum maximum-likelihood detection (VPS-QMLD), and quantum multiple-symbol detection (VPS-QMSD). System performance is evaluated in terms of the accepted-only quantum bit error rate (QBER), where underwater turbulence is modeled by an Erlang distribution. Analytical and semi-closed-form QBER expressions are derived for the three configurations and validated through Monte Carlo simulations for different water types and system parameters. The results show close agreement between analytical and simulation results and demonstrate that VPS-QMSD provides the best robustness against underwater turbulence, achieving the lowest QBER compared with VPS-QMLD and VPS-HD.
In this letter, we analyze the average probability of error of quantum modulation schemes in weakly turbulent quantum communication channels utilizing coherent states. Atmospheric turbulence-induced fading is a significant challenge that degrades the performance of free-space quantum communication systems. We derive and present closed-form expressions for the average probability of error for various detection methods: classical (shot-noise limited) single-photon detection, coherent detection, and the optimal quantum hypothesis-testing (Helstrom) detection for binary quantum modulation schemes. Our analysis focuses on the transmission of classical data modulated by quantum coherent states over a log-normal turbulent channel. Additionally, we discuss the lower bounds of the average capacities for Helstrom detection, providing comprehensive insights into the achievable information rates in realistic atmospheric conditions. The derived expressions show excellent agreement with numerical Monte Carlo simulations across a broad range of average transmitted photon numbers, offering valuable guidelines for the design and optimization of quantum communication systems.
Underwater quantum communication (UQC) has emerged as a promising approach for secure information transfer in oceanic environments by exploiting fundamental quantum mechanical principles. However, realizing UQC in practice remains highly challenging due to the inherently dynamic nature of the underwater optical channel, which is subject to wavelength-dependent absorption, multiple scattering, turbulence, and ambient noise—effects that collectively degrade photon transmission and induce quantum state errors. Conventional analytical models are insufficient to capture these nonlinear, time-varying channel characteristics, motivating the integration of artificial intelligence (AI) methods. Unlike previous surveys that focus narrowly on either underwater optical communications or quantum cryptography in isolation, this review uniquely synthesizes advances across quantum information science, ocean optics, and machine learning to address UQC-specific channel impairments. Specifically, we critically evaluate AI-driven approaches in three areas: (i) spatio-temporal deep learning models for data-driven channel estimation, demonstrating measurable improvements in channel prediction accuracy under realistic turbulence conditions; (ii) intelligent noise reduction and quantum error correction methods that reduce qubit error rates in high-scattering environments; and (iii) adaptive system optimization through reinforcement learning and hybrid optimization strategies that enhance operational fidelity and robustness. Based on this analysis, we identify key gaps in the field—including the absence of standardized underwater quantum datasets, limited experimental validation of AI-quantum hybrid frameworks, and the lack of end-to-end AI-quantum design tools—and outline concrete directions for future research. This review serves as a structured reference for researchers and practitioners working toward deployable, intelligent UQC systems.
This paper investigates the performance of coherent-state quantum optical wireless communication systems operating over atmospheric turbulence channels with pointing errors (PEs). The average error probability (AEP) and average achievable rate (AAR) are analyzed for on–off keying (OOK) and binary phase-shift keying (BPSK) signaling under photon-counting (PC), homodyne, and optimal Helstrom detection. The proposed framework jointly incorporates deterministic path loss, atmospheric turbulence, and PEs, and accommodates multiple statistical channel models, including Gamma-Gamma (GG), doubly inverted Gamma-Gamma (IGGG), and Fisher-Snedecor F distributions, within a unified analytical formulation. Closed-form expressions for AEP and AAR are derived via direct probability density function (PDF)-based integration of the conditional error probability, along with high-photon-number asymptotic approximations that provide insight into performance scaling behavior. Numerical results validate the analytical expressions and demonstrate the impact of PEs on system performance. The analysis further enables systematic comparison between classical and optimal quantum detection schemes and quantifies the achievable performance gains under different channel conditions. These results provide useful design insights for modulation and receiver selection in turbulent free-space optical (FSO) communication systems.
Continuous-Variable Quantum Key Distribution (CVQKD), based on quantum mechanical principles, offers theoretically unconditional security and represents a crucial direction for future secure communications. However, its application in marine environments faces challenges such as high attenuation, scattering, and turbulence in seawater, severely impacting quantum signal transmission and secure key generation efficiency. Orbital angular momentum (OAM) multiplexing technology leverages the orthogonality of photon OAM modes to transmit multiple independent quantum signals in parallel within a single spatial channel. In this scheme, each OAM mode serves as an independent sub-channel, enabling simultaneous key distribution across multiple modes, thereby significantly enhancing the system’s secure key rate and spectral efficiency. This paper proposes an OAM-multiplexed CVQKD scheme tailored for marine channels. Based on Yi’s power spectrum model for marine turbulence refractive index fluctuations, we derive expressions for OAM mode probability density and detection probability. Through system modeling and performance analysis, we investigate the impact of marine turbulence on OAM modes, as well as on the secure key rate and transmission distance of CVQKD systems. Results indicate that higher-order OAM modes exhibit more pronounced turbulence effects, leading to reduced key rates and limited transmission distances. The OAM multiplexing approach significantly enhances system key rates, providing theoretical and technical references for constructing high-rate seawater quantum communication networks.
This paper presents a practical optical communication framework that transmits binary information using distinct coherent states characterized by different mean photon numbers and detects the received signals via threshold-based photon counting. Unlike conventional approaches that often assume idealized detection environments, we rigorously analyze the performance of the proposed scheme under three realistic scenarios: (i) noise-free channels, (ii) channels impaired by additive Poisson noise, and (iii) turbulent free-space optical channels with fading and background noise. The coherent-state modulation enables energy-efficient transmission in the quantum-limited regime while the photon-counting receiver employs a statistically optimized decision threshold to discriminate between received photon-count levels. To address the lack of instantaneous channel state information in fading environments, we further propose a pilot-based channel estimation method that enables adaptive threshold selection. Closed-form expressions for decision thresholds and error probabilities are derived, and the effectiveness of the scheme is validated through detailed numerical simulations. These results offer design insights for photon-efficient, low-power optical communication systems operating under realistic physical impairments.