<p>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.</p>