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arXiv:2401.13243 · Quantum Information Processing

Continuous variable-based quantum communication in the ocean

Ramniwas Meena, Subhashish Banerjee

Published Jan 30, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Continuous Variable-Based Quantum Cryptography (CV-QKD) is an emerging field in quantum information science, offering unprecedented security for communication protocols by harnessing the principles of quantum mechanics. However, ocean environments pose unique challenges to quantum communication due to their distinct properties and characteristics. This work investigates the impact of turbulence on the transmission of Gaussian light beams used in a continuous variable-based quantum key distribution system for underwater quantum communication. The objective is to quantitatively analyze the induced losses and propose methodologies to mitigate their effects. To achieve this, we adopt the widely accepted ABCD matrix formalism, which provides a comprehensive framework for characterizing the propagation of optical beams through different media. Moreover, a numerical simulation framework is developed to assess the resulting losses and evaluate the performance of the proposed system. The implications of these numerical simulation frameworks for the design and optimization of quantum communication systems for oceanic environments are thoroughly discussed.

DOI
10.1007/s11128-025-04664-2

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Abstract Continuous Variable-Based Quantum Cryptography (CV-QKD) is an emerging field in quantum information science, offering unprecedented security for communication protocols by harnessing the principles of quantum mechanics. However, ocean environments pose unique challenges to quantum communication due to their distinct properties and characteristics. This work investigates the impact of turbulence on the transmission of Gaussian light beams used in a continuous variable-based quantum key distribution system for underwater quantum communication. The objective is to quantitatively analyze the induced losses and propose methodologies to mitigate their effects. To achieve this, we adopt the widely accepted ABCD matrix formalism, which provides a comprehensive framework for characterizing the propagation of optical beams through different media. Moreover, a numerical simulation framework is developed to assess the resulting losses and evaluate the performance of the proposed system. The implications of these numerical simulation frameworks for the design and optimization of quantum communication systems for oceanic environments are thoroughly discussed.
Continuous variable quantum key distribution (CVQKD) can be potentially implemented through seawater channels, whereas the involved oceanic turbulence has a negative effect on the maximal transmission distance of quantum communication systems. Here, we demonstrate the effects of the oceanic turbulence on the performance of the CVQKD system and suggest an implementation feasibility of the passive CVQKD through the oceanic turbulence-based channel. We achieve the channel transmittance characterized by the transmission distance and depth of the seawater. Moreover, a non-Gaussian approach is used for performance improvement while counteracting the effects of excess noises on the oceanic channel. Numerical simulations show that the photon operation (PO) unit can bring reductions of excess noise when taking into account the oceanic turbulence, and hence results in performance improvement in terms of transmission distance and depth as well. The passive CVQKD explores the intrinsic field fluctuations of a thermal source without using an active scheme and hence has a promising application in chip integration for portable quantum communications.
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.
Considering the ocean water’s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable (CV) quantum key distribution (QKD) based air-to-water channel. The effects of the absorption and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle .
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.
There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) over an underwater link. In particular, we focus on analyzing the channel transmittance and detection efficiency based on Monte Carlo simulation for different water types, link distances and transceiver parameters. A comparison between the transmittance obtained by simple Beer’s law and Monte Carlo simulation reveals that the transmittance of underwater link may be severely underestimated in the previous underwater CVQKD research. The effect of the receiver aperture and field of view (FOV) on detection efficiency under different water types is further evaluated based on Monte Carlo. Simulation results show that the transmission distance of the underwater CVQKD system obtained by Monte Carlo simulation in pure sea water, clear ocean water and coastal ocean water is larger than that obtained by Beer’s law, while the key rate of the system in all types of water is smaller than that obtained by Beer’s law because the size and FOV of the receiver aperture are taken into account. By considering the practical system parameters, this paper establishes a comprehensive model for evaluating the security of underwater CVQKD systems with different system configurations.
Building an underwater quantum network is necessary for various applications such as ocean exploration, environmental monitoring, and national defense. Motivated by characteristics of the oceanic turbulence channel, we suggest a machine learning approach to predicting the channel characteristics of continuous variable (CV) quantum key distribution (QKD) in challenging seawater environments. We consider the passive continuous variable (CV) measurement-device-independent (MDI) QKD in oceanic scenarios, since the passive-state preparation scheme offers simpler linear elements for preparation, resulting in reduced interaction with the practical environment. To provide a practical reference for underwater quantum communications, we suggest a prediction of transmittance for the ocean quantum links with a given neural network as an example of machine learning algorithms. The results have a good consistency with the real data within the allowable error range; this makes the passive CVQKD more promising for commercialization and implementation.